Nuclear Physics My first eBook using Wikipedia by Billy Merchant

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Articles Atom 1 Atomic nucleus 19 Electron 24 Nuclear physics 41 Particle physics 46 Photon 52 Physics 68 Quantum mechanics 81 References Article Sources and Contributors 100 Image Sources, Licenses and Contributors 105 Article Licenses License 107 Atom 1 Atom

Helium atom

An illustration of the helium atom, depicting the nucleus (pink) and the electron cloud distribution (black). The nucleus (upper right) in helium-4 is in reality spherically symmetric and closely resembles the electron cloud, although for more complicated nuclei this is not always the case. The black bar is one angstrom (10−10 m or 100 pm).

Classification

Smallest recognized division of a chemical element

Properties

Mass range: 1.67×10−27 to 4.52×10−25 kg

Electric charge: zero (neutral), or ion charge

Diameter range: 62 pm (He) to 520 pm (Cs) (data page)

Components: Electrons and a compact nucleus of protons and neutrons

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons (except in the case of hydrogen-1, which is the only stable nuclide with no neutrons). The electrons of an atom are bound to the nucleus by the electromagnetic force. Likewise, a group of atoms can remain bound to each other by chemical bonds based on the same force, forming a molecule. An atom containing an equal number of protons and electrons is electrically neutral, otherwise it is positively or negatively charged and is known as an ion. An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element, and the number of neutrons determines the isotope of the element. Chemical atoms, which in science now carry the simple name of "atom," are minuscule objects with diameters of a few tenths of a nanometer and tiny masses proportional to the volume implied by these dimensions. Atoms can only be observed individually using special instruments such as the scanning tunneling microscope. Over 99.94% of an atom's mass is concentrated in the nucleus,[1] with protons and neutrons having roughly equal mass. Each element has at least one isotope with an unstable nucleus that can undergo radioactive decay. This can result in a transmutation that changes the number of protons or neutrons in a nucleus. Electrons that are bound to atoms possess a set of stable energy levels, or orbitals, and can undergo transitions between them by absorbing or emitting photons Atom 2

that match the energy differences between the levels. The electrons determine the chemical properties of an element, and strongly influence an atom's magnetic properties. The principles of quantum mechanics have been successfully used to model the observed properties of the atom.

Etymology The name atom comes from the Greek ἄτομος (atomos, "indivisible") from ἀ- (a-, "not") and τέμνω (temnō, "I cut"), which means uncuttable, or indivisible, something that cannot be divided further. The concept of an atom as an indivisible component of matter was first proposed by early Indian and Greek philosophers. In the 18th and 19th centuries, chemists provided a physical basis for this idea by showing that certain substances could not be further broken down by chemical methods, and they applied the ancient philosophical name of atom to the chemical entity. During the late 19th and early 20th centuries, physicists discovered subatomic components and structure inside the atom, thereby demonstrating that the chemical "atom" was divisible and that the name might not be appropriate.[2] However, it was retained. This has led to some debate about whether the ancient philosophers, who intended to refer to fundamental individual objects with their concept of "atoms," were referring to modern chemical atoms, or something more like indivisible subatomic particles such as leptons or quarks, or even some more fundamental particle that has yet to be discovered.[3]

History of atomic theory

Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny quantities has been around for millennia, but these ideas were founded in abstract, philosophical reasoning rather than experimentation and empirical observation. The nature of atoms in philosophy varied considerably over time and between cultures and schools, and often had spiritual elements. Nevertheless, the basic idea of the atom was adopted by scientists thousands of years later because it elegantly explained new discoveries in the field of chemistry.[4] The ancient name of "atom" from atomism had already been nearly universally used to describe chemical atoms by that time, and it was therefore retained as a term, long after chemical atoms were found to be divisible, and even after smaller, truly indivisible particles were identified. References to the concept of atoms date back to ancient Greece and India. In India, the Ājīvika, Jain, and Cārvāka schools of atomism may date back to the 6th century BCE.[5] The Nyaya and Vaisheshika schools later developed theories on how atoms combined into more complex objects.[6] In the West, the references to atoms emerged in the 5th century BCE with Leucippus, whose student, Democritus, systematized his views. In approximately 450 BCE, Democritus coined the term átomos (Greek: ἄτομος), which means "uncuttable" or "the smallest indivisible particle of matter". Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name coined by Democritus.[4] Corpuscularianism is the postulate, expounded in the 13th-century by the alchemist Pseudo-Geber (Geber),[7] sometimes identified with Paul of Taranto, that all physical bodies possess an inner and outer layer of minute particles or corpuscles.[8] Corpuscularianism is similar to the theory of atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided. In this manner, for example, it was theorized that mercury could penetrate into metals and modify their inner structure. Corpuscularianism stayed a dominant theory over the next several hundred years. In 1661, natural philosopher Robert Boyle published The Sceptical Chymist in which he argued that matter was composed of various combinations of different "corpuscules" or atoms, rather than the classical elements of air, earth, fire and water.[9] During the 1670s corpuscularianism was used by Isaac Newton in his development of the corpuscular theory of light.[8] Atom 3

Origin of scientific theory

Further progress in the understanding of atoms did not occur until the science of chemistry began to develop. In 1789, French nobleman and scientific researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry. In 1805, English instructor and natural philosopher John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers (the law of multiple proportions) and why certain gases dissolved better in water than others. He proposed that each element consists of atoms of a single, unique type, and that these atoms Various atoms and molecules as depicted in John can join together to form chemical compounds.[10][11] Dalton is Dalton's A New System of Chemical Philosophy [12] considered the originator of modern atomic theory. (1808), one of the earliest scientific works on atomic theory Dalton's atomic hypothesis did not specify the size of atoms. Common sense indicated they must be very small, but nobody knew how small. Therefore it was a major landmark when in 1865 Johann Josef Loschmidt measured the size of the molecules that make up air. An additional line of reasoning in support of particle theory (and by extension atomic theory) began in 1827 when botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically—a phenomenon that became known as "Brownian motion". J. Desaulx suggested in 1877 that the phenomenon was caused by the thermal motion of water molecules, and in 1905 Albert Einstein produced the first mathematical analysis of the motion.[13] French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory. In 1869, building upon earlier discoveries by such scientists as Lavoisier, Dmitri Mendeleev published the first functional periodic table. The table itself is a visual representation of the periodic law, which states that certain chemical properties of elements repeat periodically when arranged by atomic number.[14]

Mendeleev's first periodic table (1869) Atom 4

Subcomponents and quantum theory

The physicist J. J. Thomson, through his work on cathode rays in 1897, discovered the electron, and concluded that they were a component of every atom. Thus he overturned the belief that atoms are the indivisible, ultimate particles of matter. Thomson postulated that the low mass, negatively charged electrons were distributed throughout the atom, possibly rotating in rings, with their charge balanced by the presence of a uniform sea of positive charge. This later became known as the plum pudding model.

In 1909, Hans Geiger and Ernest Marsden, under the direction of physicist Ernest Rutherford, bombarded a sheet of gold foil with alpha rays—by then known to be positively charged helium atoms—and discovered that a small percentage of these particles were deflected A generic atomic planetary model, or the through much larger angles than was predicted using Thomson's Rutherford model proposal. Rutherford interpreted the gold foil experiment as suggesting that the positive charge of a heavy gold atom and most of its mass was concentrated in a nucleus at the center of the atom—the Rutherford model.

While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table. The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for separating atom types through his work on ionized gases, which subsequently led to the discovery of stable isotopes. Meanwhile, in 1913, physicist Niels Bohr suggested that the electrons were confined into clearly defined, quantized orbits, and could jump between these, but could not freely spiral inward or outward in intermediate states. An electron must absorb or emit specific amounts of energy to transition between these fixed orbits. When the light from a heated material was passed through a prism, it produced a multi-colored spectrum. The appearance of fixed lines in this spectrum was successfully explained by these orbital transitions.

Later in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results A Bohr model of the hydrogen atom, showing an electron jumping between fixed orbits and refined Ernest Rutherford's and Antonius Van den Broek's model, emitting a photon of energy with a specific which proposed that the atom contains in its nucleus a number of frequency positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.[15]

Chemical bonds between atoms were now explained, by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons. As the chemical properties of the elements were known to largely repeat themselves according to the periodic law,[16] in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus. The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of the atom. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split based on the direction of an Atom 5

atom's angular momentum, or spin. As this direction is random, the beam could be expected to spread into a line. Instead, the beam was split into two parts, depending on whether the atomic spin was oriented up or down. In 1924, Louis de Broglie proposed that all particles behave to an extent like waves. In 1926, Erwin Schrödinger used this idea to develop a mathematical model of the atom that described the electrons as three-dimensional waveforms rather than point particles. A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926. In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa. This model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed. The development of the mass spectrometer allowed the exact mass of atoms to be measured. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule. The explanation for these different isotopes awaited the discovery of the neutron, a neutral-charged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.

Fission, high-energy physics and condensed matter Schematic diagram of a simple mass spectrometer

In 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product. A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission. In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized. In the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies. Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.

Components

Subatomic particles Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron. However, the hydrogen-1 atom has no neutrons and a positive hydrogen ion has no electrons. The electron is by far the least massive of these particles at 9.11×10−31 kg, with a negative electrical charge and a size that is too small to be measured using available techniques.[17] Protons have a positive charge and a mass 1,836 times that of the electron, at 1.6726×10−27 kg, although this can be reduced by changes to the energy binding the proton into an atom. Neutrons have no electrical charge and have a free mass of 1,839 times the mass of Atom 6

electrons,[18] or 1.6929×10−27 kg. Neutrons and protons have comparable dimensions—on the order of 2.5×10−15 m—although the 'surface' of these particles is not sharply defined.[19] In the Standard Model of physics, electrons are truly elementary particles with no internal structure. However, both protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +2⁄ ) and one down quark (with a charge of −1⁄ ). Neutrons consist of one up quark and two down quarks. This 3 3 distinction accounts for the difference in mass and charge between the two particles. The quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.

Nucleus

All the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 3√A fm, where A is the total number of nucleons.[20] This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more

powerful than the electrostatic force The binding energy needed for a nucleon to escape the nucleus, for various isotopes that causes positively charged protons to repel each other.[21]

Atoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay. The neutron and the proton are different types of fermions. The Pauli exclusion principle is a quantum mechanical effect that prohibits identical fermions, such as multiple protons, from occupying the same quantum physical state at the same time. Thus every proton in the nucleus must occupy a different state, with its own energy level, and the same rule applies to all of the neutrons. This prohibition does not apply to a proton and neutron occupying the same quantum state. For atoms with low atomic numbers, a nucleus that has a different number of protons than neutrons can potentially drop to a lower energy state through a radioactive decay that causes the number of protons and neutrons to more closely match. As a result, atoms with roughly matching numbers of protons and neutrons are more stable against decay. However, with increasing atomic number, the mutual repulsion of the protons requires an increasing proportion of neutrons to maintain the stability of the nucleus, which modifies this trend. Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z = 20 (calcium); and as Z increases toward the heaviest nuclei, the ratio of neutrons per proton required for stability increases to about 1.5. Atom 7

The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus. Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.

If the mass of the nucleus following a fusion reaction is less than the Illustration of a nuclear fusion process that forms sum of the masses of the separate particles, then the difference between a deuterium nucleus, consisting of a proton and a these two values can be emitted as a type of usable energy (such as a neutron, from two protons. A positron (e+)—an gamma ray, or the kinetic energy of a beta particle), as described by antimatter electron—is emitted along with an Albert Einstein's mass–energy equivalence formula, E = mc2, where m electron neutrino. is the mass loss and c is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.[22]

The fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together. It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.

Electron cloud

The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.

Electrons, like other particles, have properties of both a particle and a A potential well, showing, according to classical wave. The electron cloud is a region inside the potential well where mechanics, the minimum energy V(x) needed to each electron forms a type of three-dimensional standing wave—a reach each position x. Classically, a particle with wave form that does not move relative to the nucleus. This behavior is energy E is constrained to a range of positions between x and x . defined by an atomic orbital, a mathematical function that characterises 1 2 the probability that an electron appears to be at a particular location when its position is measured. Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form. Orbitals can have one or more ring or node structures, and they differ from each other in size, shape and orientation. Atom 8

Each atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in

Wave functions of the first five atomic orbitals. a higher energy state can drop to a lower energy state while radiating The three 2p orbitals each display a single the excess energy as a photon. These characteristic energy values, angular node that has an orientation and a defined by the differences in the energies of the quantum states, are minimum at the center. responsible for atomic spectral lines.

The amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom, compared to 2.23 million eV for splitting a deuterium nucleus. Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are

How atoms are constructed from electron orbitals farthest from the nucleus may be transferred to other nearby atoms or and link to the periodic table shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.[23]

Properties

Nuclear properties By definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form, also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element ununoctium. All known isotopes of elements with atomic numbers greater than 82 are radioactive.[24] About 339 nuclides occur naturally on Earth, of which 254 (about 75%) have not been observed to decay, and are referred to as "stable isotopes". However, only 90 of these nuclides are stable to all decay, even in theory. Another 164 (bringing the total to 254) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as "stable". An additional 34 radioactive nuclides have half-lives longer than 80 million years, and are long-lived enough to be present from the birth of the solar system. This collection of 288 nuclides are known as primordial nuclides. Finally, an additional 51 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or else as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).[25] For 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.[26]Wikipedia:Citing sources Stability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain "magic numbers" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, Atom 9

confers unusual stability on the nuclide. Of the 254 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd-odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd-odd nuclei are highly unstable with respect to beta decay, because the decay products are even-even, and are therefore more strongly bound, due to nuclear pairing effects.Wikipedia:Citing sources

Mass The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. The mass number is a simple whole number, and has units of "nucleons." An example of use of a mass number is "carbon-12," which has 12 nucleons (six protons and six neutrons). The actual mass of an atom at rest is often expressed using the unified atomic mass unit (u), which is also called a dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately 1.66×10−27 kg. Hydrogen-1, the lightest isotope of hydrogen and the atom with the lowest mass, has an atomic weight of 1.007825 u. The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the mass of the atomic mass unit. However, this number will not be an exact whole number except in the case of carbon-12 (see below). The heaviest stable atom is lead-208,[24] with a mass of 207.9766521 u. As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about 6.022×1023). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 u, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.[]Wikipedia:Citing sources

Shape and size Atoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus. However, this assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin. On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right). Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.[27] When subjected to external fields, like an electrical field, the shape of an atom may deviate from that of a sphere. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites. Significant ellipsoidal deformations have recently been shown to occur for sulfur ions in pyrite-type compounds. Atomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they can not be viewed using an optical microscope. However, individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width. A single drop of water contains about 2 sextillion (2×1021) atoms of oxygen, and twice the number of hydrogen atoms.[28] A single carat diamond with a mass of 2×10−4 kg contains about 10 sextillion (1022) atoms of carbon.[29] If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.[30] Atom 10

Radioactive decay

Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm. The most common forms of radioactive decay are:[31] • Alpha decay: this process is caused when the nucleus emits an alpha particle, which is a helium nucleus consisting of two protons and two neutrons. The result of the emission is a new element with a lower atomic number. • Beta decay (and electron capture): these processes are regulated by the weak force, and result from a transformation of a neutron into a proton, or a proton into a neutron. The neutron to proton transition is accompanied by the emission of an This diagram shows the half-life (T ) of various isotopes with Z protons and N ½ electron and an antineutrino, while neutrons. proton to neutron transition (except in electron capture) causes the emission of a positron and a neutrino. The electron or positron emissions are called beta particles. Beta decay either increases or decreases the atomic number of the nucleus by one. Electron capture is more common than positron emission, because it requires less energy. In this type of decay, an electron is absorbed by the nucleus, rather than a positron emitted from the nucleus. A neutrino is still emitted in this process, and a proton changes to a neutron. • Gamma decay: this process results from a change in the energy level of the nucleus to a lower state, resulting in the emission of electromagnetic radiation. The excited state of a nucleus which results in gamma emission usually occurs following the emission of an alpha or a beta particle. Thus, gamma decay usually follows alpha or beta decay. Other more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion— a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission. Each radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth. Atom 11

Magnetic moment Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or "spin-½". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin. The magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field. However, the most dominant contribution comes from spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons. In ferromagnetic elements such as iron, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field. The nucleus of an atom can also have a net spin. Normally these nuclei are aligned in random directions because of thermal equilibrium. However, for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.[32]

Energy levels

The potential energy of an electron in an atom is negative, its dependence of its position reaches the minimum (the most absolute value) inside the nucleus, and vanishes when the distance from the nucleus goes to infinity, roughly in an inverse proportion to the distance. In the quantum-mechanical model, a bound electron can only occupy a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for theoretical explanation. An energy level can These electron's energy levels (not to scale) are be measured by the amount of energy needed to unbind the electron sufficient for ground states of atoms up to 2 10 from the atom, and is usually given in units of electronvolts (eV). The cadmium (5s 4d ) inclusively. Do not forget that even the top of the diagram is lower than an lowest energy state of a bound electron is called the ground unbound electron state. state,Wikipedia:Please clarify while an electron transition to a higher level results in an excited state. The electron's energy raises when n increases because the (average) distance to the nucleus increases. Dependence of the energy on ℓ is caused not by electrostatic potential of the nucleus, but by interaction between electrons.

For an electron to transition between two different states, it must[citation needed] absorb or emit a photon at an energy matching the difference in the potential energy of those levels. The energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum.[33] Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors. Atom 12

When a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and An example of absorption lines in a spectrum so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.

Close examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron. When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines. The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.[34] If a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.

Valence and bonding behavior The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in that shell are called valence electrons. The number of valence electrons determines the bonding behavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells. For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. However, many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds. The chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases. Atom 13

States

Quantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas. [35] Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond. Gaseous allotropes exist as well, such as dioxygen and ozone.

Snapshots illustrating the formation of a At temperatures close to absolute zero, atoms can form a Bose–Einstein condensate Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale.[36] This super-cooled collection of atoms then behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.

Identification

The scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would normally be insurmountable. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely Scanning tunneling microscope image showing packed energy levels—the Fermi level local density of states. the individual atoms making up this gold (100) surface. Reconstruction causes the surface atoms An atom can be ionized by removing one of its electrons. The electric to deviate from the bulk crystal structure and arrange in columns several atoms wide with pits charge causes the trajectory of an atom to bend when it passes through between them. a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.

A more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry. Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element. Helium was Atom 14

discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.

Origin and current state Atoms form about 4% of the total energy density of the observable Universe, with an average density of about 0.25 atoms/m3. Within a galaxy such as the Milky Way, atoms have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3.[37] The Sun is believed to be inside the Local Bubble, a region of highly ionized gas, so the density in the solar neighborhood is only about 103 atoms/m3. Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium. Up to 95% of the Milky Way's atoms are concentrated inside stars and the total mass of atoms forms about 10% of the mass of the galaxy.[38] (The remainder of the mass is an unknown dark matter.)

Formation Electrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron. Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma – a gas of positively-charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei. Since the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron; see stellar nucleosynthesis for details. Isotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation. This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected. Elements heavier than iron were produced in supernovae through the r-process and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei. Elements such as lead formed largely through the radioactive decay of heavier elements.

Earth Most of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating.[39] Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay. There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere. Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions. Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth. Transuranic elements have radioactive lifetimes shorter than the current age of the Earth[40] and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 Atom 15

possibly deposited by cosmic dust.[41] Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore. The Earth contains approximately 1.33×1050 atoms. Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals. This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.[42]

Rare and theoretical forms

Superheavy elements While isotopes with atomic numbers higher than lead (82) are known to be radioactive, an "island of stability" has been proposed for some elements with atomic numbers above 103. These superheavy elements may have a nucleus that is relatively stable against radioactive decay. The most likely candidate for a stable superheavy atom, unbihexium, has 126 protons and 184 neutrons.

Exotic matter Each particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature. However, in 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva. Other exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test the fundamental predictions of physics.

Notes [1] In the case of hydrogen-1, with a single electron and nucleon, the proton is UNIQ-math-0-19b700d988ba3161-QINU , or 99.946% of the total atomic mass. All other nuclides (isotopes of hydrogen and all other elements) have more nucleons than electrons, so the fraction of mass taken by the nucleus is significantly closer to 100% for all of these types of atoms, than for hydrogen-1. [2] Harrison 2003, pp. 123–139. [3] Lederman provides an excellent discussion of this point, and this debate. [4] Ponomarev 1993, pp. 14–15. [5] McEvilley 2002, p. 317. [6] King 1999, pp. 105–107. [7] Moran 2005, p. 146. [8] Levere 2001, p. 7. [9] Siegfried 2002, pp. 42–55. [10] Wurtz 1881, pp. 1–2. [11] Dalton 1808. [12] Roscoe 1895, pp. 129. [13] Mazo 2002, pp. 1–7. [14] Scerri 2007, pp. 10–17. [15] Pais 1986, pp. 228–230. [16] Scerri 2007, pp. 205–226. [17] Demtröder 2002, pp. 39–42. Atom 16

[18] Woan 2000, p. 8. [19] MacGregor 1992, pp. 33–37. [20] Jevremovic 2005, p. 63. [21] Pfeffer 2000, pp. 330–336. [22] Shultis & Faw 2002, pp. 10–17. [23] Smirnov 2003, pp. 249–272. [24] Sills 2003, pp. 131–134.

[25] For more recent updates see Interactive Chart of Nuclides (Brookhaven National Laboratory) (http:/ / www. nndc. bnl. gov/ chart). [26] CRC Handbook (2002). [27] Zumdahl (2002). [28] Padilla et al. (2002:32)—"There are 2,000,000,000,000,000,000,000 (that's 2 sextillion) atoms of oxygen in one drop of water—and twice as many atoms of hydrogen." [29] A carat is 200 milligrams. By definition, carbon-12 has 0.012 kg per mole. The Avogadro constant defines atoms per mole. [30] Feynman 1995, p. 5. [31] L'Annunziata 2003, pp. 3–56. [32] Liang & Haacke 1999, pp. 412–426. [33] Fowles (1989:227–233). [34] Beyer 2003, pp. 232–236. [35] Goodstein 2002, pp. 436–438. [36] Myers 2003, p. 85. [37] Choppin, Liljenzin & Rydberg 2001, p. 441. [38] Lequeux 2005, p. 4. [39] Manuel 2001, pp. 407–430, 511–519. [40] Zaider & Rossi 2001, p. 17. [41] Manuel 2001, pp. 407–430,511–519. [42] Pauling 1960, pp. 5–10.

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einleitung_hauptseite_uk. html). University of Karlsruhe. Retrieved 2008-05-12. Atomic nucleus 19 Atomic nucleus

Nuclear physics

Nucleus · Nucleons (p, n) · Nuclear force · Nuclear reaction

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911 as a result of Ernest Rutherford's interpretation of the 1909 Geiger–Marsden gold foil experiment performed by Hans Geiger and Ernest Marsden under Rutherford's direction. The proton–neutron model of nucleus was proposed by Dmitry Ivanenko in 1932. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud.

The diameter of the nucleus is in the range of 1.75 fm (1.75×10−15 m) for hydrogen (the diameter of a single proton)Wikipedia:Verifiability to about 15 fm for the heaviest atoms, such as uranium. These dimensions are much smaller than the diameter of the atom itself A model of the atomic nucleus showing it as a (nucleus + electron cloud), by a factor of about 23,000 (uranium) to compact bundle of the two types of nucleons: protons (red) and neutrons (blue). In this diagram, about 145,000 (hydrogen).[citation needed] protons and neutrons look like little balls stuck The branch of physics concerned with studying and understanding the together, but an actual nucleus (as understood by modern nuclear physics) cannot be explained like atomic nucleus, including its composition and the forces which bind it this, but only by using quantum mechanics. In a together, is called nuclear physics. nucleus which occupies a certain energy level (for example, the ground state), each nucleon has multiple locations at once. Introduction

History

The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom. The electron had already been discovered earlier by J.J. Thomson himself, and knowing that atoms are neutral, Thomson postulated that there must be a positive charge as well. In his plum pudding model, Thomson stated that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest Rutherford later devised an experiment that involved the deflection of alpha particles at a thin sheet of metal foil. He reasoned that if Thomson's model were correct, the immense alpha particles would easily pass through the foil with very little deviation in their paths. To his surprise, many of the particles were deflected at very large angles. Because the mass of alpha particles is about 8000 times that of an electron, it became apparent that a very strong force was present that allowed the particles to be deflected. He realized that the plum pudding model could not be accurate and that the deflections of the alpha particles could only be caused by a center of concentrated charge that contained most of the atom's mass. Thus, the idea of a nuclear atom—an atom with a dense center of positive charge—became justified. Atomic nucleus 20

Etymology The term nucleus is from the Latin word nucleus, a diminutive of nux ("nut"), meaning the kernel (i.e., the "small nut") inside a watery type of fruit (like a peach). In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912. The adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example, Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom is composed of the kernel and an outer atom or shell"

Nuclear makeup

The nucleus of an atom consists of protons and neutrons (two types of baryons) bound by the nuclear force (also known as the residual strong force). These baryons are further composed of subatomic fundamental particles known as quarks bound by the strong interaction. Which chemical element an atom represents is determined by the number of protons in the nucleus. Each proton carries a single positive charge, and the total electrical charge of the nucleus is spread fairly uniformly throughout its body, with a fall-off at the edge.

Major exceptions to this rule are the light elements hydrogen and helium, where the charge is concentrated most highly at the single central point (without a central volume of uniform charge). This configuration is the same as for 1s electrons A figurative depiction of the helium-4 atom with the electron cloud in shades of in atomic orbitals, and is the expected gray. In the nucleus, the two protons and two neutrons are depicted in red and blue. This depiction shows the particles as separate, whereas in an actual helium atom, density distribution for fermions (in this the protons are superimposed in space and most likely found at the very center of case, protons) in 1s states without orbital the nucleus, and the same is true of the two neutrons. Thus, all four particles are angular momentum. most likely found in exactly the same space, at the central point. Classical images of separate particles fail to model known charge distributions in very small nuclei. As each proton carries a unit of charge, the A more accurate image is that the spatial distribution of nucleons in helium's charge distribution is indicative of the nucleus, although on a far smaller scale, is much closer to the helium electron proton distribution. The neutron distribution cloud shown here, than to the fanciful nucleus image. probably is similar. While protons define the entire charge of a nucleus and, hence, its chemical identity, neutrons are electrically neutral, but contribute to the mass of a nucleus to the same extent. Neutrons explain the phenomenon of isotopes – varieties of a chemical element which differ in atomic mass.

Protons and neutrons

Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They sometimes are viewed as two different quantum states of the same particle, the nucleon. Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit bosonic behavior when they become loosely bound in Atomic nucleus 21

pairs. In the rare case of a hypernucleus, a third baryon called a hyperon, with a different value of the strangeness quantum number can also share the wave function. However, the latter type of nuclei are extremely unstable and are not found on Earth except in high energy physics experiments. The neutron has a positively charged core of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and 2 fm. The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.

Forces Nuclei are bound together by the residual strong force (nuclear force). The residual strong force is a minor residuum of the strong interaction which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms (such as van der Waals forces that act between two inert gas atoms) are much weaker than the electromagnetic forces that hold the parts of the atoms internally together (for example, the forces that hold the electrons in an inert gas atom bound to its nucleus). The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons which is due to the electromagnetic force, thus allowing nuclei to exist. However, because the residual strong force has a limited range because it decays quickly with distance (see Yukawa potential), only nuclei smaller than a certain size can be completely stable. The largest known completely stable (e.g., stable to alpha, beta, and gamma decay) nucleus is lead-208 which contains a total of 208 nucleons (126 neutrons and 82 protons). Nuclei larger than this maximal size of 208 particles are unstable and (as a trend) become increasingly short-lived with larger size, as the number of neutrons and protons which compose them increases beyond this number. However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha decay of any known isotope, estimated at a billion times longer than the age of the universe. The residual strong force is effective over a very short range (usually only a few fermis; roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between protons and neutrons to form [NP] deuteron, and also between protons and protons, and neutrons and neutrons.

Halo nuclei and strong force range limits The effective absolute limit of the range of the strong force is represented by halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of neutrons, orbit at distances of about ten fermis (roughly similar to the 8 fermi radius of the nucleus of uranium-238). These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the chart of the nuclides—the neutron drip line and proton drip line—and are all unstable with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of less than 8.6 milliseconds. Halos in effect represent an excited state with nucleons in an outer quantum shell which has unfilled energy levels "below" it (both in terms of radius and energy). The halo may be made of either neutrons [NN, NNN] or protons [PP, PPP]. Nuclei which have a single neutron halo include 11Be and 19C. A two-neutron halo is exhibited by 6He, 11Li, 17B, 19B and 22C. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). 8He and 14Be both exhibit a four-neutron halo. Nuclei which have a proton halo include 8B and 26P. A two-proton halo is exhibited by 17Ne and 27S. Proton halos are expected to be more rare and unstable than the neutron examples, because of the repulsive electromagnetic forces of the excess proton(s). Atomic nucleus 22

Nuclear models Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, theoretically generating predictions from it is much more difficult than for most other areas of particle physics. This is essentially because perturbation theory, a widely used mathematical tool, is not applicable to quantum chromodynamics (the theory of the strong force) at the energy scales relevant to the nucleus. As a result, experiments have historically been compared to relatively crude models which are necessarily imperfect. None of these models completely explain experimental data on nuclear structure. The nuclear radius (R) is considered to be one of the basic quantities that any model must predict. For stable nuclei (not halo nuclei or other unstable distorted nuclei) the nuclear radius is roughly proportional to the cube root of the mass number (A) of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations: The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,

where A = Atomic mass number (the number of protons Z, plus the number of neutrons N) and r = 1.25 fm = 1.25 × 10−15 m. In this equation, the constant r varies by 0.2 fm, depending on the nucleus in 0 0 question, but this is less than 20% change from a constant. In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).[citation needed]

Liquid drop models Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together cause behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but it does not explain the special stability which occurs when nuclei have special "magic numbers" of protons or neutrons.

Shell models and other quantum models A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells. In the above models, the nucleons may occupy orbitals in pairs, due to being fermions, which allows to explain even/odd Z and N effects well-known from experiments. The exact nature and capacity of nuclear shells differs from those of electrons in atomic orbitals, primarily because the potential well in which the nucleons move (especially in larger nuclei) is quite different from the central electromagnetic potential well which binds electrons in atoms. Some resemblance to atomic orbital models may be seen in a small atomic nucleus like that of helium-4, in which the two protons and two neutrons separately occupy 1s orbitals analogous to the 1s orbital for the two electrons in the helium atom, and achieve unusual stability for the same reason. Nuclei with 5 nucleons are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton hydrogen-3 is unstable and will decay into helium-3 when isolated. Weak nuclear stability with 2 nucleons {NP} in the 1s orbital is found in the deuteron hydrogen-2, with only one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion, the {NP} deuteron is a boson and thus does not Atomic nucleus 23

follow Pauli Exclusion for close packing within shells. Lithium-6 with 6 nucleons is highly stable without a closed second 1p shell orbital. For light nuclei with total nucleon numbers 1 to 6 only those with 5 do not show some evidence of stability. Observations of beta-stability of light nuclei outside closed shells indicate that nuclear stability is much more complex than simple closure of shell orbitals with magic numbers of protons and neutrons. For larger nuclei, the shells occupied by nucleons begin to differ significantly from electron shells, but nevertheless, present nuclear theory does predict the magic numbers of filled nuclear shells for both protons and neutrons. The closure of the stable shells predicts unusually stable configurations, analogous to the noble group of nearly-inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element. Similarly, the distance from shell-closure explains the unusual instability of isotopes which have far from stable numbers of these particles, such as the radioactive elements 43 (technetium) and 61 (promethium), each of which is preceded and followed by 17 or more stable elements. There are however problems with the shell model when an attempt is made to account for nuclear properties well away from closed shells. This has led to complex post hoc distortions of the shape of the potential well to fit experimental data, but the question remains whether these mathematical manipulations actually correspond to the spatial deformations in real nuclei. Problems with the shell model have led some to propose realistic two-body and three-body nuclear force effects involving nucleon clusters and then build the nucleus on this basis. Two such cluster models are the Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.

Consistency between models As with the case of superfluid liquid helium, atomic nuclei are an example of a state in which both (1) "ordinary" particle physical rules for volume and (2) non-intuitive quantum mechanical rules for a wave-like nature apply. In superfluid helium, the helium atoms have volume, and essentially "touch" each other, yet at the same time exhibit strange bulk properties, consistent with a Bose–Einstein condensation. The latter reveals that they also have a wave-like nature and do not exhibit standard fluid properties, such as friction. For nuclei made of hadrons which are fermions, the same type of condensation does not occur, yet nevertheless, many nuclear properties can only be explained similarly by a combination of properties of particles with volume, in addition to the frictionless motion characteristic of the wave-like behavior of objects trapped in Erwin Schrödinger's quantum orbitals.

References

External links

• The Nucleus – a chapter from an online textbook (http:/ / www. lightandmatter. com/ html_books/ 4em/ ch02/

ch02. html)

• The LIVEChart of Nuclides – IAEA (http:/ / www-nds. iaea. org/ livechart) in Java (http:/ / www-nds. iaea. org/

livechart) or HTML (http:/ / www-nds. iaea. org/ relnsd/ vcharthtml/ VChartHTML. html)

• Article on the "nuclear shell model," giving nuclear shell filling for the various elements (http:/ / www.

halexandria. org/ dward472. htm). Accessed Sept. 16, 2009.

• Timeline: Subatomic Concepts, Nuclear Science & Technology (http:/ / nagysandor. eu/ nuklearis/ timeline/

index. html). Electron 24 Electron

Electron

Experiments with a Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the Maltese-cross-shaped target is projected against the tube face at right by a beam of electrons.

Composition Elementary particle

Statistics Fermionic

Generation First

Interactions Gravity, Electromagnetic, Weak

Symbol e−, β−

Antiparticle Positron (also called antielectron)

Theorized Richard Laming (1838–1851), G. Johnstone Stoney (1874) and others.

Discovered J. J. Thomson (1897)

Mass 9.10938291(40)×10−31 kg 5.4857990946(22)×10−4 u [1] [1,822.8884845(14)]−1 u 0.510998928(11) MeV/c2

[2] Electric charge −1 e −1.602176565(35)×10−19 C −4.80320451(10)×10−10 esu

Magnetic moment −1.00115965218076(27) μ B

Spin 1⁄ 2

The electron (symbol: e−) is a subatomic particle with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value in units of ħ, which means that it is a fermion. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Electrons also have properties of both particles and waves, and so can collide with other particles and can be diffracted like light. Experiments with electrons best demonstrate this duality because electrons have a tiny mass. Electron 25

Many physical phenomena involve electrons in an essential role, such as electricity, magnetism, and thermal conductivity, and they also participate in gravitational, electromagnetic and weak interactions. An electron moving relative to an observer generates a magnetic field; external magnetic fields will deflect an electron. Electrons radiate or absorb energy in the form of photons when accelerated. The antiparticle of the electron is called the positron; it is identical to the electron except that it carries electrical and other charges of the opposite sign. When an electron collides with a positron, both particles may be totally annihilated, producing gamma ray photons. The interaction between positive atomic nuclei (composed of protons and neutrons) and electrons through Coulomb force, compose atoms. Ionization or changes in the proportions of particles changes the binding energy of the system. The exchange or sharing of the electrons between two or more atoms is the main cause of chemical bonding. British natural philosopher Richard Laming first hypothesized the concept of an indivisible quantity of electric charge to explain the chemical properties of atoms in 1838; Irish physicist George Johnstone Stoney named this charge 'electron' in 1891, and J. J. Thomson and his team of British physicists identified it as a particle in 1897.[3] Laboratory instruments are capable of containing and observing individual electrons as well as electron plasma, whereas dedicated telescopes can detect electron plasma in outer space. Electrons may be absorbed during nucleosynthesis in stars. Electrons may be created through beta decay of radioactive isotopes and in high-energy collisions, for instance when cosmic rays enter the atmosphere. Electrons have many applications, including in electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors and particle accelerators.

History The ancient Greeks noticed that amber attracted small objects when rubbed with fur. Along with lightning, this phenomenon is one of humanity's earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the New Latin term electricus, to refer to this property of attracting small objects after being rubbed. Both electric and electricity are derived from the Latin ēlectrum (also the root of the alloy of the same name), which came from the Greek word for amber, ήλεκτρον (ēlektron). In the early 1700s, Francis Hauksbee and French chemist Charles François de Fay independently discovered what they believed to be two kinds of frictional electricity; one generated from rubbing glass, the other from rubbing resin. From this, Du Fay theorized that electricity consists of two electrical fluids, "vitreous" and "resinous", that are separated by friction and that neutralize each other when combined. A decade later Benjamin Franklin proposed that electricity was not from different types of electrical fluid, but the same electrical fluid under different pressures. He gave them the modern charge nomenclature of positive and negative respectively. Franklin thought of the charge carrier as being positive, but he did not correctly identify which situation was a surplus of the charge carrier, and which situation was a deficit. Between 1838 and 1851, British natural philosopher Richard Laming developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit electric charges. Beginning in 1846, German physicist William Weber theorized that electricity was composed of positively and negatively charged fluids, and their interaction was governed by the inverse square law. After studying the phenomenon of electrolysis in 1874, Irish physicist George Johnstone Stoney suggested that there existed a "single definite quantity of electricity", the charge of a monovalent ion. He was able to estimate the value of this elementary charge e by means of Faraday's laws of electrolysis. However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicist Hermann von Helmholtz argued that both positive and negative charges were divided into elementary parts, each of which "behaves like atoms of electricity". In 1891 Stoney coined the term electron to describe these elementary charges, writing later in 1894: "... an estimate was made of the actual amount of this most remarkable fundamental unit of electricity, for which I have since ventured to suggest the name electron". The word electron is a combination of the words electr(ic) and (i)on.[4] The suffix -on which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived Electron 26

from electron.

Discovery

The German physicist Johann Wilhelm Hittorf studied electrical conductivity in rarefied gases: in 1869, he discovered a glow emitted from the cathode that increased in size with decrease in gas pressure. In 1876, the German physicist Eugen Goldstein showed that the rays from this glow cast a shadow, and he dubbed the rays cathode rays.[5] During the 1870s, the English chemist and physicist Sir William Crookes developed the first cathode ray tube to have a high vacuum inside. He then showed that the luminescence rays appearing within the A beam of electrons deflected in a circle by a tube carried energy and moved from the cathode to the anode. magnetic field Furthermore, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged.[6] In 1879, he proposed that these properties could be explained by what he termed 'radiant matter'. He suggested that this was a fourth state of matter, consisting of negatively charged molecules that were being projected with high velocity from the cathode.

The German-born British physicist Arthur Schuster expanded upon Crookes' experiments by placing metal plates parallel to the cathode rays and applying an electric potential between the plates. The field deflected the rays toward the positively charged plate, providing further evidence that the rays carried negative charge. By measuring the amount of deflection for a given level of current, in 1890 Schuster was able to estimate the charge-to-mass ratio of the ray components. However, this produced a value that was more than a thousand times greater than what was expected, so little credence was given to his calculations at the time.[7] In 1892 Hendrik Lorentz suggested that the mass of these particles (electrons) could be a consequence of their electric charge.[8] In 1896, the British physicist J. J. Thomson, with his colleagues John S. Townsend and H. A. Wilson, performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. Thomson made good estimates of both the charge e and the mass m, finding that cathode ray particles, which he called "corpuscles," had perhaps one thousandth of the mass of the least massive ion known: hydrogen. He showed that their charge to mass ratio, e/m, was independent of cathode material. He further showed that the negatively charged particles produced by radioactive materials, by heated materials and by illuminated materials were universal. The name electron was again proposed for these particles by the Irish physicist George F. Fitzgerald, and the name has since gained universal acceptance. While studying naturally fluorescing minerals in 1896, the French physicist Henri Becquerel discovered that they emitted radiation without any exposure to an external energy source. These radioactive materials became the subject of much interest by scientists, including the New Zealand physicist Ernest Rutherford who discovered they emitted particles. He designated these particles alpha and beta, on the basis of their ability to penetrate matter. In 1900, Becquerel showed that the beta rays emitted by radium could be deflected by an electric field, and that their mass-to-charge ratio was the same as for cathode rays. This evidence strengthened the view that electrons existed as components of atoms.[9] The electron's charge was more carefully measured by the American physicists Robert Millikan and Harvey Fletcher in their oil-drop experiment of 1909, the results of which were published in 1911. This experiment used an electric field to prevent a charged droplet of oil from falling as a result of gravity. This device could measure the electric charge from as few as 1–150 ions with an error margin of less than 0.3%. Comparable experiments had been done earlier by Thomson's team, using clouds of charged water droplets generated by electrolysis, and in 1911 by Abram Ioffe, who independently obtained the same result as Millikan using charged microparticles of metals, then published Electron 27

his results in 1913.[10] However, oil drops were more stable than water drops because of their slower evaporation rate, and thus more suited to precise experimentation over longer periods of time. Around the beginning of the twentieth century, it was found that under certain conditions a fast-moving charged particle caused a condensation of supersaturated water vapor along its path. In 1911, Charles Wilson used this principle to devise his cloud chamber, allowing the tracks of charged particles, such as fast-moving electrons, to be photographed.

Atomic theory

By 1914, experiments by physicists Ernest Rutherford, Henry Moseley, James Franck and Gustav Hertz had largely established the structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons. In 1913, Danish physicist Niels Bohr postulated that electrons resided in quantized energy states, with the energy determined by the angular momentum of the electron's orbits about the nucleus. The electrons could move between these states, or orbits, by the emission or absorption of photons at specific frequencies. By means of these quantized orbits, he accurately explained the spectral lines of the hydrogen atom. However, Bohr's model failed to account for the relative intensities of the spectral lines and it was unsuccessful in explaining the spectra of more complex atoms. The Bohr model of the atom, showing states of electron with energy quantized by the number n. Chemical bonds between atoms were explained by Gilbert Newton An electron dropping to a lower orbit emits a Lewis, who in 1916 proposed that a covalent bond between two atoms photon equal to the energy difference between the orbits. is maintained by a pair of electrons shared between them. Later, in 1927, Walter Heitler and Fritz London gave the full explanation of the electron-pair formation and chemical bonding in terms of quantum mechanics. In 1919, the American chemist Irving Langmuir elaborated on the Lewis' static model of the atom and suggested that all electrons were distributed in successive "concentric (nearly) spherical shells, all of equal thickness". The shells were, in turn, divided by him in a number of cells each containing one pair of electrons. With this model Langmuir was able to qualitatively explain the chemical properties of all elements in the periodic table, which were known to largely repeat themselves according to the periodic law.

In 1924, Austrian physicist Wolfgang Pauli observed that the shell-like structure of the atom could be explained by a set of four parameters that defined every quantum energy state, as long as each state was inhabited by no more than a single electron. (This prohibition against more than one electron occupying the same quantum energy state became known as the Pauli exclusion principle.) The physical mechanism to explain the fourth parameter, which had two distinct possible values, was provided by the Dutch physicists Samuel Goudsmit and George Uhlenbeck. In 1925, Goudsmit and Uhlenbeck suggested that an electron, in addition to the angular momentum of its orbit, possesses an intrinsic angular momentum and magnetic dipole moment. The intrinsic angular momentum became known as spin, and explained the previously mysterious splitting of spectral lines observed with a high-resolution spectrograph; this phenomenon is known as fine structure splitting. Electron 28

Quantum mechanics In his 1924 dissertation Recherches sur la théorie des quanta (Research on Quantum Theory), French physicist Louis de Broglie hypothesized that all matter possesses a de Broglie wave similar to light. That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment. Wave-like nature is observed, for example, when a beam of light is passed through parallel slits and creates interference patterns. In 1927, the interference effect was found in a beam of electrons by English physicist George Paget Thomson with a thin metal film and by American physicists Clinton Davisson and Lester Germer using a crystal of nickel. De Broglie's prediction of a wave nature for electrons led Erwin Schrödinger to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the Schrödinger equation, successfully described how electron waves propagated. Rather than yielding a solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position near where the electron was bound in space, for which the electron wave equations did not change in time. This approach led to a second formulation of quantum mechanics (the first being by Heisenberg in 1925), and solutions of Schrödinger's equation, like Heisenberg's, provided derivations of the energy states of an electron in a hydrogen atom that were equivalent to those that had been derived first by Bohr in 1913, and that were known to reproduce the hydrogen spectrum. Once spin and the interaction between multiple In quantum mechanics, the behavior of an electrons were considered, quantum mechanics later allowed the electron in an atom is described by an orbital, which is a probability distribution rather than an configuration of electrons in atoms with higher atomic numbers than orbit. In the figure, the shading indicates the hydrogen to be successfully predicted. relative probability to "find" the electron, having the energy corresponding to the given quantum In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a numbers, at that point. model of the electron – the Dirac equation, consistent with relativity theory, by applying relativistic and symmetry considerations to the hamiltonian formulation of the quantum mechanics of the electro-magnetic field. In order to resolve some problems within his relativistic equation, in 1930 Dirac developed a model of the vacuum as an infinite sea of particles having negative energy, which was dubbed the Dirac sea. This led him to predict the existence of a positron, the antimatter counterpart of the electron. This particle was discovered in 1932 by Carl Anderson, who proposed calling standard electrons negatrons, and using electron as a generic term to describe both the positively and negatively charged variants.

In 1947 Willis Lamb, working in collaboration with graduate student Robert Retherford, found that certain quantum states of hydrogen atom, which should have the same energy, were shifted in relation to each other, the difference being the Lamb shift. About the same time, Polykarp Kusch, working with Henry M. Foley, discovered the magnetic moment of the electron is slightly larger than predicted by Dirac's theory. This small difference was later called anomalous magnetic dipole moment of the electron. This difference was later explained by the theory of quantum electrodynamics, developed by Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman in the late 1940s. Electron 29

Particle accelerators With the development of the particle accelerator during the first half of the twentieth century, physicists began to delve deeper into the properties of subatomic particles. The first successful attempt to accelerate electrons using electromagnetic induction was made in 1942 by Donald Kerst. His initial betatron reached energies of 2.3 MeV, while subsequent betatrons achieved 300 MeV. In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at General Electric. This radiation was caused by the acceleration of electrons, moving near the speed of light, through a magnetic field. With a beam energy of 1.5 GeV, the first high-energy particle collider was ADONE, which began operations in 1968. This device accelerated electrons and positrons in opposite directions, effectively doubling the energy of their collision when compared to striking a static target with an electron. The Large Electron–Positron Collider (LEP) at CERN, which was operational from 1989 to 2000, achieved collision energies of 209 GeV and made important measurements for the Standard Model of particle physics.

Confinement of individual electrons Individual electrons can now be easily confined in ultra small (L=20 nm, W=20 nm) CMOS transistors operated at cryogenic temperature over a range of −269 °C (4 K) to about −258 °C (15 K). The electron wavefunction spreads in a semiconductor lattice and negligibly interacts with the valence band electrons, so it can be treated in the single particle formalism, by replacing its mass with the effective mass tensor.

Characteristics

Classification

In the Standard Model of particle physics, electrons belong to the group of subatomic particles called leptons, which are believed to be fundamental or elementary particles. Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the first-generation of fundamental particles. The second and third generation contain charged leptons, the muon and the tau, which are identical to the electron in charge, spin and interactions, but are more massive. Leptons differ from the other basic constituent of matter, the quarks, by their lack of strong interaction. All members of Standard Model of elementary particles. The electron is at lower left. the lepton group are fermions, because they all have half-odd integer spin; the electron has spin 1⁄ . 2 Electron 30

Fundamental properties The invariant mass of an electron is approximately 9.109×10−31 kilograms, or 5.489×10−4 atomic mass units. On the basis of Einstein's principle of mass–energy equivalence, this mass corresponds to a rest energy of 0.511 MeV. The ratio between the mass of a proton and that of an electron is about 1836. Astronomical measurements show that the proton-to-electron mass ratio has held the same value for at least half the age of the universe, as is predicted by the Standard Model. Electrons have an electric charge of −1.602×10−19 coulomb,[] which is used as a standard unit of charge for subatomic particles, and is also called the elementary charge. This elementary charge has a relative standard uncertainty of 2.2×10−8.[] Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign. As the symbol e is used for the elementary charge, the electron is commonly symbolized by e−, where the minus sign indicates the negative charge. The positron is symbolized by e+ because it has the same properties as the electron but with a positive rather than negative charge. The electron has an intrinsic angular momentum or spin of 1⁄ . This property is usually stated by referring to the 2 electron as a spin-1⁄ particle. For such particles the spin magnitude is √3⁄ ħ.[11] while the result of the measurement 2 2 of a projection of the spin on any axis can only be ±ħ⁄ . In addition to spin, the electron has an intrinsic magnetic 2 moment along its spin axis. It is approximately equal to one Bohr magneton,[12] which is a physical constant equal to 9.27400915(23)×10−24 joules per tesla. The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as helicity. The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent. Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters. There is a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[13] There are elementary particles that spontaneously decay into less massive particles. An example is the muon, which decays into an electron, a neutrino and an antineutrino, with a mean lifetime of 2.2×10−6 seconds. However, the electron is thought to be stable on theoretical grounds: the electron is the least massive particle with non-zero electric charge, so its decay would violate charge conservation. The experimental lower bound for the electron's mean lifetime is 4.6×1026 years, at a 90% confidence level.

Quantum properties As with all particles, electrons can act as waves. This is called the wave–particle duality and can be demonstrated using the double-slit experiment. The wave-like nature of the electron allows it to pass through two parallel slits simultaneously, rather than just one slit as would be the case for a classical particle. In quantum mechanics, the wave-like property of one particle can be described mathematically as a complex-valued function, the wave function, commonly denoted by the Greek letter psi (ψ). When the absolute value of this function is squared, it gives the probability that a particle will be observed near a location—a probability density. Electron 31

Electrons are identical particles because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ(r , r ) = −ψ(r , r ), where the variables r and r 1 2 2 1 1 2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. Bosons, such as the photon, have symmetric wave Example of an antisymmetric wave function for a quantum state of two identical fermions in a functions instead. 1-dimensional box. If the particles swap position, the wave function inverts its sign. In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.

Virtual particles Physicists believe that empty space may be continually creating pairs of virtual particles, such as a positron and electron, which rapidly annihilate each other shortly thereafter. The combination of the energy variation needed to create these particles, and the time during which they exist, fall under the threshold of detectability expressed by the Heisenberg uncertainty relation, ΔE · Δt ≥ ħ. In effect, the energy needed to create these virtual particles, ΔE, can be "borrowed" from the vacuum for a period of time, Δt, so that their product is no more than the reduced Planck constant, ħ ≈ 6.6×10−16 eV·s. Thus, for a virtual electron, Δt is at most 1.3×10−21 s. While an electron–positron virtual pair is in existence, the coulomb force from the ambient electric field surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes what is called vacuum polarization. In effect, the vacuum behaves like a medium having a dielectric permittivity more than unity. Thus the effective charge of an electron is actually smaller than its true value, and the charge decreases with increasing distance from the electron. This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN A schematic depiction of virtual particle accelerator. Virtual particles cause a comparable shielding electron–positron pairs appearing at random near [14] effect for the mass of the electron. an electron (at lower left) The interaction with virtual particles also explains the small (about 0.1%) deviation of the intrinsic magnetic moment of the electron from the Bohr magneton (the anomalous magnetic moment). The extraordinarily precise agreement of this predicted difference with the experimentally determined value is viewed as one of the great achievements of quantum electrodynamics. In classical physics, the angular momentum and magnetic moment of an object depend upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties might seem inconsistent. The apparent paradox can be explained by the formation of virtual photons in the electric field generated by the electron. These photons cause the electron to shift about in a jittery fashion (known as zitterbewegung), which results in a net circular motion with precession. This motion produces both the spin and the magnetic moment of the electron. In Electron 32

atoms, this creation of virtual photons explains the Lamb shift observed in spectral lines.

Interaction An electron generates an electric field that exerts an attractive force on a particle with a positive charge, such as the proton, and a repulsive force on a particle with a negative charge. The strength of this force is determined by Coulomb's inverse square law. When an electron is in motion, it generates a magnetic field.[15] The Ampère-Maxwell law relates the magnetic field to the mass motion of electrons (the current) with respect to an observer. It is this property of induction which supplies the magnetic field that drives an electric motor. The electromagnetic field of an arbitrary moving charged particle is expressed by the Liénard–Wiechert potentials, which are valid even when the particle's speed is close to that of light (relativistic). When an electron is moving through a magnetic field, it is subject to the Lorentz force that exerts an influence in a direction perpendicular to the plane defined by the magnetic field and the electron velocity. This centripetal force causes the electron to follow a helical trajectory through the field at a radius called the gyroradius. The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation.[16][17] The energy emission in turn causes a recoil of the electron, known as the Abraham–Lorentz–Dirac Force, which creates a friction that slows the electron. This force is caused by a back-reaction of the electron's own field upon itself. A particle with charge q (at left) is moving with Photons mediate electromagnetic interactions between particles in velocity v through a magnetic field B that is oriented toward the viewer. For an electron, q is quantum electrodynamics. An isolated electron at a constant velocity negative so it follows a curved trajectory toward cannot emit or absorb a real photon; doing so would violate the top. conservation of energy and momentum. Instead, virtual photons can transfer momentum between two charged particles. This exchange of virtual photons, for example, generates the Coulomb force. Energy emission can occur when a moving electron is deflected by a charged particle, such as a proton. The acceleration of the electron results in the emission of Bremsstrahlung radiation.

An inelastic collision between a photon (light) and a solitary (free) electron is called Compton scattering. This collision results in a transfer of momentum and energy between the particles, which modifies the wavelength of the photon by an amount called the Compton shift.[18] The maximum magnitude of this wavelength shift is h/m c, which is known as the Compton wavelength. For an electron, it e has a value of 2.43×10−12 m. When the wavelength of the light is long (for instance, the wavelength of the visible light is 0.4–0.7 μm) the wavelength shift becomes negligible. Such interaction between the light and free electrons is called Thomson scattering or Linear Thomson scattering.

The relative strength of the electromagnetic interaction between two charged particles, such as an electron and a proton, is given by the

Here, Bremsstrahlung is produced by an electron fine-structure constant. This value is a dimensionless quantity formed e deflected by the electric field of an atomic by the ratio of two energies: the electrostatic energy of attraction (or nucleus. The energy change E − E determines 2 1 repulsion) at a separation of one Compton wavelength, and the rest the frequency f of the emitted photon. energy of the charge. It is given by α ≈ 7.297353×10−3, which is approximately equal to 1⁄ . 137 Electron 33

When electrons and positrons collide, they annihilate each other, giving rise to two or more gamma ray photons. If the electron and positron have negligible momentum, a positronium atom can form before annihilation results in two or three gamma ray photons totalling 1.022 MeV. On the other hand, high-energy photons may transform into an electron and a positron by a process called pair production, but only in the presence of a nearby charged particle, such as a nucleus. In the theory of electroweak interaction, the left-handed component of electron's wavefunction forms a weak isospin doublet with the electron neutrino. This means that during weak interactions, electron neutrinos behave like electrons. Either member of this doublet can undergo a charged current interaction by emitting or absorbing a W and be converted into the other member. Charge is conserved during this reaction because the W boson also carries a charge, canceling out any net change during the transmutation. Charged current interactions are responsible for the phenomenon of beta decay in a radioactive atom. Both the electron and electron neutrino can undergo a neutral current interaction via a Z0 exchange, and this is responsible for neutrino-electron elastic scattering.

Atoms and molecules

An electron can be bound to the nucleus of an atom by the attractive Coulomb force. A system of one or more electrons bound to a nucleus is called an atom. If the number of electrons is different from the nucleus' electrical charge, such an atom is called an ion. The wave-like behavior of a bound electron is described by a function called an atomic orbital. Each orbital has its own set of quantum numbers such as energy, angular momentum and projection of angular momentum, and only a discrete set of these orbitals exist around the nucleus. According to the Pauli exclusion principle each orbital can be occupied by up to two electrons, which must differ in their spin quantum number.

Electrons can transfer between different orbitals Probability densities for the first few hydrogen atom orbitals, seen in by the emission or absorption of photons with an cross-section. The energy level of a bound electron determines the orbital it energy that matches the difference in potential. occupies, and the color reflects the probability to find the electron at a given position. Other methods of orbital transfer include collisions with particles, such as electrons, and the Auger effect. In order to escape the atom, the energy of the electron must be increased above its binding energy to the atom. This occurs, for example, with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron.

The orbital angular momentum of electrons is quantized. Because the electron is charged, it produces an orbital magnetic moment that is proportional to the angular momentum. The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus. The magnetic moment of the nucleus is negligible compared with that of the electrons. The magnetic moments of the electrons that occupy the same orbital (so called, paired electrons) cancel each other out. The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics. The strongest bonds are formed by the sharing or transfer of electrons between atoms, allowing the formation of molecules. Within a molecule, electrons move under the influence of several nuclei, and occupy Electron 34

molecular orbitals; much as they can occupy atomic orbitals in isolated atoms. A fundamental factor in these molecular structures is the existence of electron pairs. These are electrons with opposed spins, allowing them to occupy the same molecular orbital without violating the Pauli exclusion principle (much like in atoms). Different molecular orbitals have different spatial distribution of the electron density. For instance, in bonded pairs (i.e. in the pairs that actually bind atoms together) electrons can be found with the maximal probability in a relatively small volume between the nuclei. On the contrary, in non-bonded pairs electrons are distributed in a large volume around nuclei.

Conductivity

If a body has more or fewer electrons than are required to balance the positive charge of the nuclei, then that object has a net electric charge. When there is an excess of electrons, the object is said to be negatively charged. When there are fewer electrons than the number of protons in nuclei, the object is said to be positively charged. When the number of electrons and the number of protons are equal, their charges cancel each other and the object is said to be electrically neutral. A macroscopic body can develop an electric charge through rubbing, by the triboelectric effect.

Independent electrons moving in vacuum are termed free electrons. Electrons in metals also behave as if they were free. In reality the particles that are commonly termed electrons in metals and other solids A lightning discharge consists primarily of a flow are quasi-electrons—quasiparticles, which have the same electrical of electrons. The electric potential needed for charge, spin and magnetic moment as real electrons but may have a lightning may be generated by a triboelectric different mass. When free electrons—both in vacuum and effect. metals—move, they produce a net flow of charge called an electric current, which generates a magnetic field. Likewise a current can be created by a changing magnetic field. These interactions are described mathematically by Maxwell's equations.

At a given temperature, each material has an electrical conductivity that determines the value of electric current when an electric potential is applied. Examples of good conductors include metals such as copper and gold, whereas glass and Teflon are poor conductors. In any dielectric material, the electrons remain bound to their respective atoms and the material behaves as an insulator. Most semiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation. On the other hand, metals have an electronic band structure containing partially filled electronic bands. The presence of such bands allows electrons in metals to behave as if they were free or delocalized electrons. These electrons are not associated with specific atoms, so when an electric field is applied, they are free to move like a gas (called Fermi gas) through the material much like free electrons. Because of collisions between electrons and atoms, the drift velocity of electrons in a conductor is on the order of millimeters per second. However, the speed at which a change of current at one point in the material causes changes in currents in other parts of the material, the velocity of propagation, is typically about 75% of light speed. This occurs because electrical signals propagate as a wave, with the velocity dependent on the dielectric constant of the material. Metals make relatively good conductors of heat, primarily because the delocalized electrons are free to transport thermal energy between atoms. However, unlike electrical conductivity, the thermal conductivity of a metal is nearly independent of temperature. This is expressed mathematically by the Wiedemann–Franz law, which states that the ratio of thermal conductivity to the electrical conductivity is proportional to the temperature. The thermal disorder in the metallic lattice increases the electrical resistivity of the material, producing a temperature dependence for electrical current. Electron 35

When cooled below a point called the critical temperature, materials can undergo a phase transition in which they lose all resistivity to electrical current, in a process known as superconductivity. In BCS theory, this behavior is modeled by pairs of electrons entering a quantum state known as a Bose–Einstein condensate. These Cooper pairs have their motion coupled to nearby matter via lattice vibrations called phonons, thereby avoiding the collisions with atoms that normally create electrical resistance. (Cooper pairs have a radius of roughly 100 nm, so they can overlap each other.) However, the mechanism by which higher temperature superconductors operate remains uncertain. Electrons inside conducting solids, which are quasi-particles themselves, when tightly confined at temperatures close to absolute zero, behave as though they had split into three other quasiparticles: spinons, Orbitons and holons. The former carries spin and magnetic moment, the next carries its orbital location while the latter electrical charge.

Motion and energy According to Einstein's theory of special relativity, as an electron's speed approaches the speed of light, from an observer's point of view its relativistic mass increases, thereby making it more and more difficult to accelerate it from within the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in a vacuum, c. However, when relativistic electrons—that is, electrons moving at a speed close to c—are injected into a dielectric medium such as water, where the local speed of light is significantly less than c, the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called Cherenkov radiation. The effects of special relativity are based on a quantity known as the Lorentz factor, defined as where v is the speed of the particle. The kinetic energy K of an electron moving with velocity v is: e

where m is the mass of electron. For example, the Stanford linear e accelerator can accelerate an electron to roughly 51 GeV. Since an electron behaves as a wave, at a given velocity it has a characteristic de Broglie wavelength. This is given by λ = h/p where h is the Planck e constant and p is the momentum. For the 51 GeV electron above, the wavelength is about 2.4×10−17 m, small enough to explore structures well below the size of an atomic nucleus. Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as v approaches c.

Formation Electron 36

The Big Bang theory is the most widely accepted scientific theory to explain the early stages in the evolution of the Universe. For the first millisecond of the Big Bang, the temperatures were over 10 billion Kelvin and photons had mean energies over a million electronvolts. These photons were sufficiently energetic that they could react with each other to form pairs of electrons and positrons. Likewise, positron-electron pairs annihilated each other and emitted energetic photons:

γ + γ ↔ e+ + e− Pair production caused by the collision of a An equilibrium between electrons, positrons and photons was photon with an atomic nucleus maintained during this phase of the evolution of the Universe. After 15 seconds had passed, however, the temperature of the universe dropped below the threshold where electron-positron formation could occur. Most of the surviving electrons and positrons annihilated each other, releasing gamma radiation that briefly reheated the universe. For reasons that remain uncertain, during the process of leptogenesis there was an excess in the number of electrons over positrons. Hence, about one electron in every billion survived the annihilation process. This excess matched the excess of protons over antiprotons, in a condition known as baryon asymmetry, resulting in a net charge of zero for the universe. The surviving protons and neutrons began to participate in reactions with each other—in the process known as nucleosynthesis, forming isotopes of hydrogen and helium, with trace amounts of lithium. This process peaked after about five minutes. Any leftover neutrons underwent negative beta decay with a half-life of about a thousand seconds, releasing a proton and electron in the process,

n → p + e− + ν e For about the next 300,000–400,000 years, the excess electrons remained too energetic to bind with atomic nuclei. What followed is a period known as recombination, when neutral atoms were formed and the expanding universe became transparent to radiation. Roughly one million years after the big bang, the first generation of stars began to form. Within a star, stellar nucleosynthesis results in the production of positrons from the fusion of atomic nuclei. These antimatter particles immediately annihilate with electrons, releasing gamma rays. The net result is a steady reduction in the number of electrons, and a matching increase in the number of neutrons. However, the process of stellar evolution can result in the synthesis of radioactive isotopes. Selected isotopes can subsequently undergo negative beta decay, emitting an electron and antineutrino from the nucleus. An example is the cobalt-60 (60Co) isotope, which decays to form nickel-60 (60Ni). Electron 37

At the end of its lifetime, a star with more than about 20 solar masses can undergo gravitational collapse to form a black hole. According to classical physics, these massive stellar objects exert a gravitational attraction that is strong enough to prevent anything, even electromagnetic radiation, from escaping past the Schwarzschild radius. However, quantum mechanical effects are believed to potentially allow the emission of Hawking radiation at this distance. Electrons (and positrons) are thought to be created at the event horizon of these stellar remnants.

When pairs of virtual particles (such as an An extended air shower generated by an energetic cosmic ray striking the Earth's atmosphere electron and positron) are created in the vicinity of the event horizon, the random spatial distribution of these particles may permit one of them to appear on the exterior; this process is called quantum tunnelling. The gravitational potential of the black hole can then supply the energy that transforms this virtual particle into a real particle, allowing it to radiate away into space. In exchange, the other member of the pair is given negative energy, which results in a net loss of mass-energy by the black hole. The rate of Hawking radiation increases with decreasing mass, eventually causing the black hole to evaporate away until, finally, it explodes.

Cosmic rays are particles traveling through space with high energies. Energy events as high as 3.0×1020 eV have been recorded. When these particles collide with nucleons in the Earth's atmosphere, a shower of particles is generated, including pions. More than half of the cosmic radiation observed from the Earth's surface consists of muons. The particle called a muon is a lepton which is produced in the upper atmosphere by the decay of a pion.

π− → μ− + ν μ A muon, in turn, can decay to form an electron or positron.

μ− → e− + ν e + ν μ

Observation

Remote observation of electrons requires detection of their radiated energy. For example, in high-energy environments such as the corona of a star, free electrons form a plasma that radiates energy due to Bremsstrahlung radiation. Electron gas can undergo plasma oscillation, which is waves caused by synchronized variations in electron density, and these produce energy emissions that can be detected by using radio telescopes.

The frequency of a photon is proportional to its energy. As a bound Aurorae are mostly caused by energetic electrons electron transitions between different energy levels of an atom, it will precipitating into the atmosphere. Electron 38

absorb or emit photons at characteristic frequencies. For instance, when atoms are irradiated by a source with a broad spectrum, distinct absorption lines will appear in the spectrum of transmitted radiation. Each element or molecule displays a characteristic set of spectral lines, such as the hydrogen spectral series. Spectroscopic measurements of the strength and width of these lines allow the composition and physical properties of a substance to be determined. In laboratory conditions, the interactions of individual electrons can be observed by means of particle detectors, which allow measurement of specific properties such as energy, spin and charge. The development of the Paul trap and Penning trap allows charged particles to be contained within a small region for long durations. This enables precise measurements of the particle properties. For example, in one instance a Penning trap was used to contain a single electron for a period of 10 months. The magnetic moment of the electron was measured to a precision of eleven digits, which, in 1980, was a greater accuracy than for any other physical constant. The first video images of an electron's energy distribution were captured by a team at Lund University in Sweden, February 2008. The scientists used extremely short flashes of light, called attosecond pulses, which allowed an electron's motion to be observed for the first time. The distribution of the electrons in solid materials can be visualized by angle-resolved photoemission spectroscopy (ARPES). This technique employs the photoelectric effect to measure the reciprocal space—a mathematical representation of periodic structures that is used to infer the original structure. ARPES can be used to determine the direction, speed and scattering of electrons within the material.

Plasma applications

Particle beams

Electron beams are used in welding. They allow energy densities up to 107 W·cm−2 across a narrow focus diameter of 0.1–1.3 mm and usually require no filler material. This welding technique must be performed in a vacuum to prevent the electrons from interacting with the gas before reaching their target, and it can be used to join conductive materials that would otherwise be considered unsuitable for welding.

Electron-beam lithography (EBL) is a method of etching semiconductors at resolutions smaller than a micron. This technique is limited by high costs, slow performance, the need to operate the beam in the vacuum and the tendency of the electrons to scatter in solids. During a NASA wind tunnel test, a model of the Space Shuttle is targeted by a beam of electrons, The last problem limits the resolution to about 10 nm. For this reason, simulating the effect of ionizing gases during EBL is primarily used for the production of small numbers of re-entry. specialized integrated circuits.

Electron beam processing is used to irradiate materials in order to change their physical properties or sterilize medical and food products. Electron beams fluidise or quasi-melt glasses without significant increase of temperature on intensive irradiation: e.g. intensive electron radiation causes a many orders of magnitude decrease of viscosity and stepwise decrease of its activation energy.[19] Linear particle accelerators generate electron beams for treatment of superficial tumors in radiation therapy. Electron therapy can treat such skin lesions as basal-cell carcinomas because an electron beam only penetrates to a limited depth before being absorbed, typically up to 5 cm for electron energies in the range 5–20 MeV. An electron beam can be used to supplement the treatment of areas that have been irradiated by X-rays. Particle accelerators use electric fields to propel electrons and their antiparticles to high energies. These particles emit synchrotron radiation as they pass through magnetic fields. The dependency of the intensity of this radiation upon spin polarizes the electron beam—a process known as the Sokolov–Ternov effect.[20] Polarized electron beams Electron 39

can be useful for various experiments. Synchrotron radiation can also cool the electron beams to reduce the momentum spread of the particles. Electron and positron beams are collided upon the particles' accelerating to the required energies; particle detectors observe the resulting energy emissions, which particle physics studies .

Imaging Low-energy electron diffraction (LEED) is a method of bombarding a crystalline material with a collimated beam of electrons and then observing the resulting diffraction patterns to determine the structure of the material. The required energy of the electrons is typically in the range 20–200 eV. The reflection high-energy electron diffraction (RHEED) technique uses the reflection of a beam of electrons fired at various low angles to characterize the surface of crystalline materials. The beam energy is typically in the range 8–20 keV and the angle of incidence is 1–4°. The electron microscope directs a focused beam of electrons at a specimen. Some electrons change their properties, such as movement direction, angle, and relative phase and energy as the beam interacts with the material. Microscopists can record these changes in the electron beam to produce atomically resolved images of the material. In blue light, conventional optical microscopes have a diffraction-limited resolution of about 200 nm. By comparison, electron microscopes are limited by the de Broglie wavelength of the electron. This wavelength, for example, is equal to 0.0037 nm for electrons accelerated across a 100,000-volt potential. The Transmission Electron Aberration-Corrected Microscope is capable of sub-0.05 nm resolution, which is more than enough to resolve individual atoms. This capability makes the electron microscope a useful laboratory instrument for high resolution imaging. However, electron microscopes are expensive instruments that are costly to maintain. Two main types of electron microscopes exist: transmission and scanning. Transmission electron microscopes function like overhead projectors, with a beam of electrons passing through a slice of material then being projected by lenses on a photographic slide or a charge-coupled device. Scanning electron microscopes rasteri a finely focused electron beam, as in a TV set, across the studied sample to produce the image. Magnifications range from 100× to 1,000,000× or higher for both microscope types. The scanning tunneling microscope uses quantum tunneling of electrons from a sharp metal tip into the studied material and can produce atomically resolved images of its surface.

Other applications In the free-electron laser (FEL), a relativistic electron beam passes through a pair of undulators that contain arrays of dipole magnets whose fields point in alternating directions. The electrons emit synchrotron radiation that coherently interacts with the same electrons to strongly amplify the radiation field at the resonance frequency. FEL can emit a coherent high-brilliance electromagnetic radiation with a wide range of frequencies, from microwaves to soft X-rays. These devices may find manufacturing, communication and various medical applications, such as soft tissue surgery. Electrons are important in cathode ray tubes, which have been extensively used as display devices in laboratory instruments, computer monitors and television sets. In a photomultiplier tube, every photon striking the photocathode initiates an avalanche of electrons that produces a detectable current pulse. Vacuum tubes use the flow of electrons to manipulate electrical signals, and they played a critical role in the development of electronics technology. However, they have been largely supplanted by solid-state devices such as the transistor. Electron 40

Notes [1] The fractional version's denominator is the inverse of the decimal value (along with its relative standard uncertainty of ). [2] The electron's charge is the negative of elementary charge, which has a positive value for the proton. [3] Dahl (1997:122–185).

[4] "electron, n.2". OED Online. March 2013. Oxford University Press. Accessed 12 April 2013 (http:/ / www. oed. com/ view/ Entry/

60302?rskey=owKYbt& result=2) [5] Dahl (1997:55–58). [6] Dahl (1997:64–78). [7] Dahl (1997:99).

[8] Frank Wilczek: " Happy Birthday, Electron (http:/ / www. scientificamerican. com/ article. cfm?id=happy-birthday-electron)" Scientific American, June 2012. [9] Buchwald and Warwick (2001:90–91). [10] Original publication in Russian: [11] This magnitude is obtained from the spin quantum number as UNIQ-math-0-19b700d988ba3161-QINU for quantum number s = . See: [12] Bohr magneton: UNIQ-math-1-19b700d988ba3161-QINU [13] The classical electron radius is derived as follows. Assume that the electron's charge is spread uniformly throughout a spherical volume. Since one part of the sphere would repel the other parts, the sphere contains electrostatic potential energy. This energy is assumed to equal the electron's rest energy, defined by special relativity (E = mc2). From electrostatics theory, the potential energy of a sphere with radius r and charge e is given by: UNIQ-math-2-19b700d988ba3161-QINU where ε is the vacuum permittivity. For an electron with rest mass m , the rest energy is equal to: 0 0 UNIQ-math-3-19b700d988ba3161-QINU where c is the speed of light in a vacuum. Setting them equal and solving for r gives the classical electron radius. See: [14] —lists a 9% mass difference for an electron that is the size of the Planck distance. [15] Munowitz (2005:140). [16] Munowitz (2005:160). [17] Radiation from non-relativistic electrons is sometimes termed cyclotron radiation. [18] The change in wavelength, Δλ, depends on the angle of the recoil, θ, as follows, UNIQ-math-4-19b700d988ba3161-QINU where c is the speed of light in a vacuum and m is the electron mass. See Zombeck (2007: 393, 396). e [19] Mobus G. et al. (2010). Journal of Nuclear Materials, v. 396, 264–271, doi:10.1016/j.jnucmat.2009.11.020 [20] The polarization of an electron beam means that the spins of all electrons point into one direction. In other words, the projections of the spins of all electrons onto their momentum vector have the same sign.

References

External links

• "The Discovery of the Electron" (http:/ / www. aip. org/ history/ electron/ ). American Institute of Physics, Center for History of Physics.

• "Particle Data Group" (http:/ / pdg. lbl. gov/ ). University of California.

• Bock, R.K.; Vasilescu, A. (1998). The Particle Detector BriefBook (http:/ / physics. web. cern. ch/ Physics/

ParticleDetector/ BriefBook/ ) (14th ed.). Springer. ISBN 3-540-64120-3.

• Copeland, Ed. "Spherical Electron" (http:/ / www. sixtysymbols. com/ videos/ electron_sphere. htm). Sixty Symbols. Brady Haran for the University of Nottingham. Nuclear physics 41 Nuclear physics

Nuclear physics

Nucleus · Nucleons (p, n) · Nuclear force · Nuclear reaction

Nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology. The field of particle physics evolved out of nuclear physics and is typically taught in close association with nuclear physics.

History

Modern physics

Schrödinger equation

History of modern physics

The history of nuclear physics as a discipline distinct from atomic physics starts with the discovery of radioactivity by Henri Becquerel in 1896, while investigating phosphorescence in uranium salts. The discovery of the electron by J. J. Thomson a year later was an indication that the atom had internal structure. At the turn of the 20th century the accepted model of the atom was J. J. Thomson's plum pudding model in which the atom was a large positively charged ball with small negatively charged electrons embedded inside of it. By the turn of the century physicists had also discovered three types of radiation emanating from atoms, which they named alpha, beta, and gamma radiation. Experiments in 1911 by Otto Hahn, and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete. That is, electrons were ejected from the atom with a range of energies, rather than the discrete amounts of energies that were observed in gamma and alpha decays. This was a problem for nuclear physics at the time, because it indicated that energy was not conserved in these decays. In 1905, Albert Einstein formulated the idea of mass–energy equivalence. While the work on radioactivity by Becquerel and Marie Curie predates this, an explanation of the source of the energy of radioactivity would have to wait for the discovery that the nucleus itself was composed of smaller constituents, the nucleons. Nuclear physics 42

Rutherford's team discovers the nucleus

In 1907 Ernest Rutherford published "Radiation of the α Particle from Radium in passing through Matter."[1] Hans Geiger expanded on this work in a communication to the Royal Society[2] with experiments he and Rutherford had done, passing α particles through air, aluminum foil and gold leaf. More work was published in 1909 by Geiger and Marsden[3] and further greatly expanded work was published in 1910 by Geiger,[4] In 1911-2 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it.

The key experiment behind this announcement happened in 1910 at the University of Manchester, as Ernest Rutherford's team performed a remarkable experiment in which Hans Geiger and Ernest Marsden under his supervision fired alpha particles (helium nuclei) at a thin film of gold foil. The plum pudding model predicted that

the alpha particles should come out of the foil with their Ernest Rutherford is often considered to be the "Father of trajectories being at most slightly bent. Rutherford had the Nuclear Physics" idea to instruct his team to look for something that shocked him to actually observe: a few particles were scattered through large angles, even completely backwards, in some cases. He likened it to firing a bullet at tissue paper and having it bounce off. The discovery, beginning with Rutherford's analysis of the data in 1911, eventually led to the Rutherford model of the atom, in which the atom has a very small, very dense nucleus containing most of its mass, and consisting of heavy positively charged particles with embedded electrons in order to balance out the charge (since the neutron was unknown). As an example, in this model (which is not the modern one) nitrogen-14 consisted of a nucleus with 14 protons and 7 electrons (21 total particles), and the nucleus was surrounded by 7 more orbiting electrons.

The Rutherford model worked quite well until studies of nuclear spin were carried out by Franco Rasetti at the California Institute of Technology in 1929. By 1925 it was known that protons and electrons had a spin of 1/2, and in the Rutherford model of nitrogen-14, 20 of the total 21 nuclear particles should have paired up to cancel each other's spin, and the final odd particle should have left the nucleus with a net spin of 1/2. Rasetti discovered, however, that nitrogen-14 had a spin of 1.

James Chadwick discovers the neutron In 1932 Chadwick realized that radiation that had been observed by Walther Bothe, Herbert Becker, Irène and Frédéric Joliot-Curie was actually due to a neutral particle of about the same mass as the proton, that he called the neutron (following a suggestion about the need for such a particle, by Rutherford). In the same year Dmitri Ivanenko suggested that neutrons were in fact spin 1/2 particles and that the nucleus contained neutrons to explain the mass not due to protons, and that there were no electrons in the nucleus—only protons and neutrons. The neutron spin immediately solved the problem of the spin of nitrogen-14, as the one unpaired proton and one unpaired neutron in this model, each contribute a spin of 1/2 in the same direction, for a final total spin of 1. With the discovery of the neutron, scientists at last could calculate what fraction of binding energy each nucleus had, from comparing the nuclear mass with that of the protons and neutrons which composed it. Differences between nuclear masses were calculated in this way and—when nuclear reactions were measured—were found to agree with Nuclear physics 43

Einstein's calculation of the equivalence of mass and energy to high accuracy (within 1 percent as of in 1934).

Proca's equations of the massive vector boson field Alexandru Proca was the first to develop and report the massive vector boson field equations and a theory of the mesonic field of nuclear forces. Proca's equations were known to Wolfgang Pauli[5] who mentioned the equations in his Nobel address, and they were also known to Yukawa, Wentzel, Taketani, Sakata, Kemmer, Heitler, and Fröhlich who appreciated the content of Proca's equations for developing a theory of the atomic nuclei in Nuclear Physics.[6][7][8][9]

Yukawa's meson postulated to bind nuclei In 1935 Hideki Yukawa proposed the first significant theory of the strong force to explain how the nucleus holds together. In the Yukawa interaction a virtual particle, later called a meson, mediated a force between all nucleons, including protons and neutrons. This force explained why nuclei did not disintegrate under the influence of proton repulsion, and it also gave an explanation of why the attractive strong force had a more limited range than the electromagnetic repulsion between protons. Later, the discovery of the pi meson showed it to have the properties of Yukawa's particle. With Yukawa's papers, the modern model of the atom was complete. The center of the atom contains a tight ball of neutrons and protons, which is held together by the strong nuclear force, unless it is too large. Unstable nuclei may undergo alpha decay, in which they emit an energetic helium nucleus, or beta decay, in which they eject an electron (or positron). After one of these decays the resultant nucleus may be left in an excited state, and in this case it decays to its ground state by emitting high energy photons (gamma decay). The study of the strong and weak nuclear forces (the latter explained by Enrico Fermi via Fermi's interaction in 1934) led physicists to collide nuclei and electrons at ever higher energies. This research became the science of particle physics, the crown jewel of which is the standard model of particle physics which describes the strong, weak, and electromagnetic forces.

Modern nuclear physics A heavy nucleus can contain hundreds of nucleons which means that with some approximation it can be treated as a classical system, rather than a quantum-mechanical one. In the resulting liquid-drop model, the nucleus has an energy which arises partly from surface tension and partly from electrical repulsion of the protons. The liquid-drop model is able to reproduce many features of nuclei, including the general trend of binding energy with respect to mass number, as well as the phenomenon of nuclear fission. Superimposed on this classical picture, however, are quantum-mechanical effects, which can be described using the nuclear shell model, developed in large part by Maria Goeppert-Mayer. Nuclei with certain numbers of neutrons and protons (the magic numbers 2, 8, 20, 28, 50, 82, 126, ...) are particularly stable, because their shells are filled. Other more complicated models for the nucleus have also been proposed, such as the interacting boson model, in which pairs of neutrons and protons interact as bosons, analogously to Cooper pairs of electrons. Much of current research in nuclear physics relates to the study of nuclei under extreme conditions such as high spin and excitation energy. Nuclei may also have extreme shapes (similar to that of Rugby balls) or extreme neutron-to-proton ratios. Experimenters can create such nuclei using artificially induced fusion or nucleon transfer reactions, employing ion beams from an accelerator. Beams with even higher energies can be used to create nuclei at very high temperatures, and there are signs that these experiments have produced a phase transition from normal nuclear matter to a new state, the quark-gluon plasma, in which the quarks mingle with one another, rather than being segregated in triplets as they are in neutrons and protons. Nuclear physics 44

Nuclear decay Eighty elements have at least one stable isotope never observed to decay, amounting to a total of about 254 stable isotopes. However, thousands of isotopes have been characterized that are unstable. These radioisotopes decay over time scales ranging from fractions of a second to weeks, years, billions of years, or even trillions of years. The stability of a nucleus is highest when it falls into a certain range or balance of composition of neutrons and protons; too few or too many neutrons may cause it to decay. For example, in beta decay a nitrogen-16 atom (7 protons, 9 neutrons) is converted to an oxygen-16 atom (8 protons, 8 neutrons) within a few seconds of being created. In this decay a neutron in the nitrogen nucleus is converted into a proton and an electron and an antineutrino by the weak interaction. The element is transmuted to another element in by acquiring the created proton. In alpha decay the radioactive element decays by emitting a helium nucleus (2 protons and 2 neutrons), giving another element, plus helium-4. In many cases this process continues through several steps of this kind, including other types of decays, until a stable element is formed. In gamma decay, a nucleus decays from an excited state into a lower energy state, by emitting a gamma ray. The element is not changed to another element in the process (no nuclear transmutation is involved). Other more exotic decays are possible (see the main article). For example, in internal conversion decay, the energy from an excited nucleus may be used to eject one of the inner orbital electrons from the atom, in a process which produces high speed electrons, but is not beta decay, and (unlike beta decay) does not transmute one element to another.

Nuclear fusion In nuclear fusion, two low mass nuclei come into very close contact with each other, so that the strong force fuses them. It requires a large amount of energy to overcome the repulsion between the nuclei for the strong or nuclear forces to produce this effect, therefore nuclear fusion can only take place at very high temperatures or high pressures. Once the process succeeds, a very large amount of energy is released and the combined nucleus assumes a lower energy level. The binding energy per nucleon increases with mass number up until nickel-62. Stars like the Sun are powered by the fusion of four protons into a helium nucleus, two positrons, and two neutrinos. The uncontrolled fusion of hydrogen into helium is known as thermonuclear runaway. A frontier in current research at various institutions, for example the Joint European Torus (JET) and ITER, is the development of an economically viable method of using energy from a controlled fusion reaction. Natural nuclear fusion is the origin of the light and energy produced by the core of all stars including our own sun.

Nuclear fission Nuclear fission is the reverse process of fusion. For nuclei heavier than nickel-62 the binding energy per nucleon decreases with the mass number. It is therefore possible for energy to be released if a heavy nucleus breaks apart into two lighter ones. The process of alpha decay is in essence a special type of spontaneous nuclear fission. This process produces a highly asymmetrical fission because the four particles which make up the alpha particle are especially tightly bound to each other, making production of this nucleus in fission particularly likely. For certain of the heaviest nuclei which produce neutrons on fission, and which also easily absorb neutrons to initiate fission, a self-igniting type of neutron-initiated fission can be obtained, in a so-called chain reaction. Chain reactions were known in chemistry before physics, and in fact many familiar processes like fires and chemical explosions are chemical chain reactions. The fission or "nuclear" chain-reaction, using fission-produced neutrons, is the source of energy for nuclear power plants and fission type nuclear bombs, such as those detonated by the United States in Hiroshima and Nagasaki, Japan, at the end of World War II. Heavy nuclei such as uranium and thorium may also undergo spontaneous fission, but they are much more likely to undergo decay by alpha decay. Nuclear physics 45

For a neutron-initiated chain-reaction to occur, there must be a critical mass of the element present in a certain space under certain conditions. The conditions for the smallest critical mass require the conservation of the emitted neutrons and also their slowing or moderation so there is a greater cross-section or probability of them initiating another fission. In two regions of Oklo, Gabon, Africa, natural nuclear fission reactors were active over 1.5 billion years ago.[citation needed] Measurements of natural neutrino emission have demonstrated that around half of the heat emanating from the Earth's core results from radioactive decay. However, it is not known if any of this results from fission chain-reactions.[citation needed]

Production of "heavy" elements (atomic number greater than five) According to the theory, as the Universe cooled after the big bang it eventually became possible for common subatomic particles as we know them (neutrons, protons and electrons) to exist. The most common particles created in the big bang which are still easily observable to us today were protons and electrons (in equal numbers). The protons would eventually form hydrogen atoms. Almost all the neutrons created in the Big Bang were absorbed into helium-4 in the first three minutes after the Big Bang, and this helium accounts for most of the helium in the universe today (see Big Bang nucleosynthesis). Some fraction of elements beyond helium were created in the Big Bang, as the protons and neutrons collided with each other (lithium, beryllium, and perhaps some boron), but all of the "heavier elements" (carbon, element number 6, and elements of greater atomic number) that we see today, were created inside of stars during a series of fusion stages, such as the proton-proton chain, the CNO cycle and the triple-alpha process. Progressively heavier elements are created during the evolution of a star. Since the binding energy per nucleon peaks around iron, energy is only released in fusion processes occurring below this point. Since the creation of heavier nuclei by fusion costs energy, nature resorts to the process of neutron capture. Neutrons(due to their lack of charge) are readily absorbed by a nucleus. The heavy elements are created by either a slow neutron capture process (the so-called s process) or by the rapid, or r process. The s process occurs in thermally pulsing stars (called AGB, or asymptotic giant branch stars) and takes hundreds to thousands of years to reach the heaviest elements of lead and bismuth. The r process is thought to occur in supernova explosions because the conditions of high temperature, high neutron flux and ejected matter are present. These stellar conditions make the successive neutron captures very fast, involving very neutron-rich species which then beta-decay to heavier elements, especially at the so-called waiting points that correspond to more stable nuclides with closed neutron shells (magic numbers).

References [1] Philosophical Magazine (12, p 134-46) [2] Proc. Roy. Soc. July 17, 1908 [3] Proc. Roy. Soc. A82 p 495-500 [4] Proc. Roy. Soc. Feb. 1, 1910 [5] W. Pauli, Nobel lecture, December 13, 1946. [6] G. A. Proca, Alexandre Proca.Oeuvre Scientifique Publiée, S.I.A.G., Rome, 1988. [7] C. Vuille, J. Ipser, J. Gallagher, “Einstein-Proca model, micro black holes, and naked singularities”, General Relativity and Gravitation, 34 (2002), 689. [8] R. Scipioni, “Isomorphism between non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of scalar gravity theories”, Class. Quantum Gravity., 16 (1999), 2471. [9] R. W. Tucker and C. Wang, C., “An Einstein-Proca-fluid model for dark matter gravitational interactions”, Nucl. Phys. B - Proc. suppl., 57 (1997) 259. Nuclear physics 46

Bibliography • Nuclear Physics by Irving Kaplan 2nd edition, 1962 Addison-Wesley • General Chemistry by Linus Pauling 1970 Dover Pub. ISBN 0-486-65622-5 • Introductory Nuclear Physics by Kenneth S. Krane Pub. Wiley

• N.D. Cook (2010). Models of the Atomic Nucleus (http:/ / www. springer. com/ physics/ particle+ and+ nuclear+

physics/ book/ 978-3-642-14736-4) (2nd ed.). Springer. pp. xvi & 324. ISBN 978-3-642-14736-4. • Ahmad, D.Sc., Ishfaq; American Institute of Physics (1996). Physics of particles and nuclei. 1-3 27 (3 ed.). University of California: American Institute of Physics Press. p. 209.

External links

• American Physical Society Division of Nuclear Physics (http:/ / dnp. aps. org)

• American Nuclear Society (http:/ / www. ans. org)

• Boiling Water Reactor Plant, BWR Simulator Program (http:/ / www. acme-nuclear. com)

• Annotated bibliography on nuclear physics from the Alsos Digital Library for Nuclear Issues (http:/ / alsos. wlu.

edu/ qsearch. aspx?browse=science/ Nuclear+ Physics)

• Nucleonica ..web driven nuclear science (http:/ / www. nucleonica. net)

• Nuclear science wiki (http:/ / www. nucleonica. net/ wiki/ index. php/ Main_Page)

• Nuclear Data Services - IAEA (http:/ / www-nds. iaea. org)

Particle physics

Standard model of particle physics

Large Hadron Collider tunnel at CERN

Particle physics is a branch of physics which studies the nature of particles that are the constituents of what is usually referred to as matter and radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics. Although the word "particle" can be used in reference to many objects (e.g. a proton, a gas particle, or even household dust), the term "particle physics" usually refers to the study of the fundamental objects of the universe – fields that must be defined in order to explain the observed particles, and that cannot be defined by a combination of other fundamental fields. The current set of fundamental fields and their dynamics are summarized in a theory called the Standard Model, therefore particle physics is largely the study of the Standard Model's particle content and its possible extensions. Particle physics 47

Subatomic particles

Modern particle physics research is focused on subatomic particles, including atomic constituents such as electrons, protons, and neutrons (protons and neutrons are composite particles called baryons, made of quarks), produced by radioactive and scattering processes, such as photons, neutrinos, and muons, as well as a wide range of exotic particles. To be specific, the term particle is a misnomer from classical physics because the dynamics of particle physics are governed by quantum mechanics. As such, they exhibit wave-particle duality, displaying particle-like behavior under certain The particle content of the Standard Model of Physics experimental conditions and wave-like behavior in others. In more technical terms, they are described by quantum state vectors in a Hilbert space, which is also treated in quantum field theory. Following the convention of particle physicists, elementary particles refer to objects such as electrons and photons as it is well known that those types of particles display wave-like properties as well.

Elementary Particles

Types Generations Antiparticle Colors Total

Quarks 2 3 Pair 3 36

Leptons 2 3 Pair None 12

Gluons 1 1 Own 8 8

W 1 1 Pair None 2

Z 1 1 Own None 1

Photon 1 1 Own None 1

Higgs 1 1 Own None 1

Total 61

All particles, and their interactions observed to date, can be described almost entirely by a quantum field theory called the Standard Model. The Standard Model has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the experimental tests conducted to date. However, most particle physicists believe that it is an incomplete description of nature, and that a more fundamental theory awaits discovery (See Theory of Everything). In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model. Particle physics 48

History

Modern physics

Schrödinger equation

History of modern physics

The idea that all matter is composed of elementary particles dates to at least the 6th century BC. The philosophical doctrine of atomism and the nature of elementary particles were studied by ancient Greek philosophers such as Leucippus, Democritus, and Epicurus; ancient Indian philosophers such as Kanada, Dignāga, and Dharmakirti; Muslim scientists such as Ibn al-Haytham, Ibn Sina, and Mohammad al-Ghazali; and in early modern Europe by physicists such as Pierre Gassendi, Robert Boyle, and Isaac Newton. The particle theory of light was also proposed by Ibn al-Haytham, Ibn Sina, Gassendi, and Newton. Those early ideas were founded through abstract, philosophical reasoning rather than experimentation and empirical observation. In the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Dalton and his contemporaries believed those were the fundamental particles of nature and thus named them atoms, after the Greek word atomos, meaning "indivisible". However, near the end of that century, physicists discovered that atoms are not, in fact, the fundamental particles of nature, but conglomerates of even smaller particles. The early 20th-century explorations of nuclear physics and quantum physics culminated in proofs of nuclear fission in 1939 by Lise Meitner (based on experiments by Otto Hahn), and nuclear fusion by Hans Bethe in that same year. Those discoveries gave rise to an active industry of generating one atom from another, even rendering possible (although it will probably never be profitable) the transmutation of lead into gold; and, those same discoveries also led to the development of nuclear weapons. Throughout the 1950s and 1960s, a bewildering variety of particles were found in scattering experiments. It was referred to as the "particle zoo". That term was deprecated after the formulation of the Standard Model during the 1970s in which the large number of particles was explained as combinations of a (relatively) small number of fundamental particles.

Standard Model The current state of the classification of all elementary particles is explained by the Standard Model. It describes the strong, weak, and electromagnetic fundamental interactions, using mediating gauge bosons. The species of gauge bosons are the gluons, W−, W+ and Z bosons, and the photons. The Standard Model also contains 24 fundamental particles, (12 particles and their associated anti-particles), which are the constituents of all matter. Finally, the Standard Model also predicted the existence of a type of boson known as the Higgs boson. Early in the morning on July 4, 2012, physicists with the Large Hadron Collider at CERN announced they have found a new particle that behaves similarly to what is expected from the Higgs boson.[1] Quarks and electrons were before this discovery not considered to be composed of other particles. However, with the discovery and verification of the existence of the Higgs boson, which gives other particles their mass, this belief has been changed. Particle physics 49

Experimental laboratories In particle physics, the major international laboratories are located at the: • Brookhaven National Laboratory (Long Island, United States). Its main facility is the Relativistic Heavy Ion Collider (RHIC), which collides heavy ions such as gold ions and polarized protons. It is the world's first heavy ion collider, and the world's only polarized proton collider.Wikipedia:Verifiability • Budker Institute of Nuclear Physics (Novosibirsk, Russia). Its main projects are now the electron-positron colliders VEPP-2000, operated since 2006, and VEPP-4, started experiments in 1994. Earlier facilities include the first electron-electron beam-beam collider VEP-1, which conducted experiments from 1964 to 1968; the electron-positron colliders VEPP-2, operated from 1965 to 1974; and, its successor VEPP-2M, performed experiments from 1974 to 2000. • CERN, (Franco-Swiss border, near Geneva). Its main project is now the Large Hadron Collider (LHC), which had its first beam circulation on 10 September 2008, and is now the world's most energetic collider of protons. It also became the most energetic collider of heavy ions after it began colliding lead ions. Earlier facilities include the Large Electron–Positron Collider (LEP), which was stopped on November 2, 2000 and then dismantled to give way for LHC; and the Super Proton Synchrotron, which is being reused as a pre-accelerator for the LHC. • DESY (Hamburg, Germany). Its main facility is the Hadron Elektron Ring Anlage (HERA), which collides electrons and positrons with protons. • Fermilab, (Batavia, United States). Its main facility until 2011 was the Tevatron, which collided protons and antiprotons and was the highest-energy particle collider on earth until the Large Hadron Collider surpassed it on 29 November 2009. • KEK, (Tsukuba, Japan). It is the home of a number of experiments such as the K2K experiment, a neutrino oscillation experiment and Belle, an experiment measuring the CP violation of B mesons. Many other particle accelerators do exist. The techniques required to do modern, experimental, particle physics are quite varied and complex, constituting a sub-specialty nearly completely distinct from the theoretical side of the field.

Theory

Quantum field theory

Feynman diagram

History

Theoretical particle physics attempts to develop the models, theoretical framework, and mathematical tools to understand current experiments and make predictions for future experiments. See also theoretical physics. There are several major interrelated efforts being made in theoretical particle physics today. One important branch attempts to better understand the Standard Model and its tests. By extracting the parameters of the Standard Model, from Particle physics 50

experiments with less uncertainty, this work probes the limits of the Standard Model and therefore expands our understanding of nature's building blocks. Those efforts are made challenging by the difficulty of calculating quantities in quantum chromodynamics. Some theorists working in this area refer to themselves as phenomenologists and they may use the tools of quantum field theory and effective field theory. Others make use of lattice field theory and call themselves lattice theorists. Another major effort is in model building where model builders develop ideas for what physics may lie beyond the Standard Model (at higher energies or smaller distances). This work is often motivated by the hierarchy problem and is constrained by existing experimental data. It may involve work on supersymmetry, alternatives to the Higgs mechanism, extra spatial dimensions (such as the Randall-Sundrum models), Preon theory, combinations of these, or other ideas. A third major effort in theoretical particle physics is string theory. String theorists attempt to construct a unified description of quantum mechanics and general relativity by building a theory based on small strings, and branes rather than particles. If the theory is successful, it may be considered a "Theory of Everything". There are also other areas of work in theoretical particle physics ranging from particle cosmology to loop quantum gravity. This division of efforts in particle physics is reflected in the names of categories on the arXiv, a preprint archive:[2] hep-th (theory), hep-ph (phenomenology), hep-ex (experiments), hep-lat (lattice gauge theory).

Practical applications In principle, all physics (and practical applications developed therefrom) can be derived from the study of fundamental particles. In practice, even if "particle physics" is taken to mean only "high-energy atom smashers", many technologies have been developed during these pioneering investigations that later find wide uses in society. Cyclotrons are used to produce medical isotopes for research and treatment (for example, isotopes used in PET imaging), or used directly for certain cancer treatments. The development of Superconductors has been pushed forward by their use in particle physics. The World Wide Web and touchscreen technology were initially developed at CERN. Additional applications are found in medicine, national security, industry, computing, science, and workforce development, illustrating a long and growing list of beneficial practical applications with contributions from particle physics.

Future The primary goal, which is pursued in several distinct ways, is to find and understand what physics may lie beyond the standard model. There are several powerful experimental reasons to expect new physics, including dark matter and neutrino mass. There are also theoretical hints that this new physics should be found at accessible energy scales. Furthermore, there may be surprises that will give us opportunities to learn about nature. Much of the effort to find this new physics are focused on new collider experiments. The Large Hadron Collider (LHC) was completed in 2008 to help continue the search for the Higgs boson, supersymmetric particles, and other new physics. An intermediate goal is the construction of the International Linear Collider (ILC), which will complement the LHC by allowing more precise measurements of the properties of newly found particles. In August 2004, a decision for the technology of the ILC was taken but the site has still to be agreed upon. In addition, there are important non-collider experiments that also attempt to find and understand physics beyond the Standard Model. One important non-collider effort is the determination of the neutrino masses, since these masses may arise from neutrinos mixing with very heavy particles. In addition, cosmological observations provide many useful constraints on the dark matter, although it may be impossible to determine the exact nature of the dark matter without the colliders. Finally, lower bounds on the very long lifetime of the proton put constraints on Grand Unified Particle physics 51

Theories at energy scales much higher than collider experiments will be able to probe any time soon.

References

[1] http:/ / www. wired. com/ wiredscience/ 2012/ 07/ higgs-boson-discovery/

[2] arxiv.org (http:/ / www. arxiv. org)

Further reading Introductory reading • Frank Close (2004) Particle Physics: A Very Short Introduction. Oxford University Press. ISBN 0-19-280434-0. • Close, Frank; Marten, Michael; Sutton, Christine (2004). The particle odyssey: a journey to the heart of the

matter (http:/ / books. google. com/ ?id=PX87qqj5B2UC& dq=rolf+ wideroe,+ lawrence). Oxford University Press. ISBN 9780198609438. • Ford, Kenneth W. (2005) The Quantum World. Harvard Univ. Press. • Oerter, Robert (2006) The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume. • Schumm, Bruce A. (2004) Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins Univ. Press. ISBN 0-8018-7971-X.

• Riazuddin. "An Overview of Particle Physics and Cosmology" (http:/ / indico. ncp. edu. pk/ indico/ getFile. py/

access?sessionId=0& resId=0& materialId=0& confId=10). NCP Journal of Physics (Dr. Professor Riazuddin, High Energy Theory Group, and senior scientist at the National Center for Nuclear Physics) 1 (1): 50. • Frank Close (2006) The New Cosmic Onion. Taylor & Francis. ISBN 1-58488-798-2. Advanced reading • Robinson, Matthew B., Gerald Cleaver, and J. R. Dittmann (2008) "A Simple Introduction to Particle Physics" -

Part 1, 135pp. (http:/ / arxiv. org/ abs/ 0810. 3328v1) and Part 2, nnnpp. (http:/ / arxiv. org/ abs/ 0908. 1395v1) Baylor University Dept. of Physics. • Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4. • Kane, Gordon L. (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5. • Perkins, Donald H. (1999). Introduction to High Energy Physics. Cambridge University Press. ISBN 0-521-62196-8. • Povh, Bogdan (1995). Particles and Nuclei: An Introduction to the Physical Concepts. Springer-Verlag. ISBN 0-387-59439-6. • Boyarkin, Oleg (2011). Advanced Particle Physics Two-Volume Set. CRC Press. ISBN 978-1-4398-0412-4.

External links

• Symmetry magazine (http:/ / www. symmetrymagazine. org)

• Fermilab (http:/ / www. fnal. gov/ )

• Particle physics – it matters (http:/ / www. iop. org/ publications/ iop/ 2009/ page_38211. html) - the Institute of Physics

• Nobes, Matthew (2002) "Introduction to the Standard Model of Particle Physics" on Kuro5hin: Part 1, (http:/ /

www. kuro5hin. org/ story/ 2002/ 5/ 1/ 3712/ 31700) Part 2, (http:/ / www. kuro5hin. org/ story/ 2002/ 5/ 14/

19363/ 8142) Part 3a, (http:/ / www. kuro5hin. org/ story/ 2002/ 7/ 15/ 173318/ 784) Part 3b. (http:/ / www.

kuro5hin. org/ story/ 2002/ 8/ 21/ 195035/ 576)

• CERN (http:/ / public. web. cern. ch/ public/ ) - European Organization for Nuclear Research

• The Particle Adventure (http:/ / particleadventure. org/ ) - educational project sponsored by the Particle Data Group of the Lawrence Berkeley National Laboratory (LBNL) Photon 52 Photon

Photon

Photons emitted in a coherent beam from a laser

Composition Elementary particle

Statistics Bosonic

Interactions Electromagnetic

Symbol γ, hν, or ħω

Theorized Albert Einstein

Mass 0 <1×10−18 eV/c2

Mean lifetime Stable

Electric charge 0 <1×10−35 e

Spin 1

Parity −1

C parity −1

Condensed I(JPC)=0,1(1−−)

A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured. The modern photon concept was developed gradually by Albert Einstein to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium. It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized (i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that light itself is quantized. In 1926 the chemist Gilbert N. Lewis coined the name photon for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that Photon 53

quanta of light have an independent existence, and Lewis' term photon for light quanta was accepted. In the Standard Model of particle physics, photons are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of photons, such as charge, mass and spin, are determined by the properties of this gauge symmetry. The photon concept has led to momentous advances in experimental and theoretical physics, such as lasers, Bose–Einstein condensation, quantum field theory, and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers and for sophisticated applications in optical communication such as quantum cryptography. In the fine arts, photons is what makes photography possible, and in biology photons enable humans and other organisms to have vision.

Nomenclature

Standard model of particle physics

Large Hadron Collider tunnel at CERN

In 1900, Max Planck was working on black-body radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum) was used even before 1900 to mean particles or amounts of different quantities, including electricity. Later, in 1905 Albert Einstein went further by suggesting that electromagnetic waves could only exist in these discrete wave-packets.[1] He called such a wave-packet the light quantum (German: das Lichtquant). The name photon derives from the Greek word for light, φῶς (transliterated phôs), and was coined[2] in 1926 by the physical chemist Gilbert Lewis, who published a speculative theory in which photons were "uncreatable and indestructible". Although Lewis' theory was never accepted as it was contradicted by many experiments, his new name, photon, was adopted immediately by most physicists. Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923. In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard, named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade. In chemistry and optical engineering, photons are usually symbolized by hν, the energy of a photon, where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f. Photon 54

Physical properties

A photon is massless,[3] has no electric charge, and is stable. A photon has two possible polarization states. In the momentum representation, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon's wave vector may not be zero and can be represented either as a spacial 3-vector or as a (relativistic) four-vector; in the latter case it belongs to the light cone (pictured). Different signs of the four-vector denote different circular polarizations, but in the 3-vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is three-dimensional.

The photon is the gauge boson for electromagnetism,[4] and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[5] Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons The cone shows possible values of wave 4-vector of various energy will be emitted, from radio waves to gamma rays. A of a photon. Green and indigo represent left and photon can also be emitted when a particle and its corresponding right polarization antiparticle are annihilated (for example, electron–positron annihilation).

In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[6]

The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):

where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[7] Since p points in the direction of the photon's propagation, the magnitude of the momentum is

The photon also carries spin angular momentum that does not depend on its frequency.[8] The magnitude of its spin is and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon.[9] To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of mass frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since it is determined, as we have seen, only by the photon's frequency or wavelength—which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net Photon 55

momentum. (However, it is possible if the system interacts with another particle or field for annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.) The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter.[10] That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus. The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.[11]

Experimental checks on photon mass The photon is currently understood to be strictly massless, but this is an experimental question. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in space-time. Thus, it would still be the speed of space-time ripples (gravitational waves and gravitons), but it would not be the speed of photons. A massive photon would have other effects as well. Coulomb's law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb's law to very high precision. A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2. Sharper upper limits have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, the magnetic field is only observable if the photon is massless. In case of a massive photon, the mass term would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2. The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring. Such methods were used to obtain the sharper upper limit of 10−18eV/c2 (the equivalent of 1.07×10−27 atomic mass units) given by the Particle Data Group.[12] These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.[13] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb's law is valid. Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors. Photon 56

Historical development

In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637), Robert Hooke (1665), and Christian Huygens (1678);[14] however, particle models remained dominant, chiefly due to the influence of Isaac Newton. In the early nineteenth century, Thomas Young and Thomas Young's double-slit experiment in 1805 August Fresnel clearly demonstrated the interference and showed that light can act as a wave, helping to defeat early particle theories of light. diffraction of light and by 1850 wave models were generally accepted. In 1865, James Clerk Maxwell's prediction[15] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves—seemed to be the final blow to particle models of light.

The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave higher than a certain threshold; light of model of electromagnetic radiation, leading to the idea that light-energy was packaged frequency lower than the threshold, no into quanta described by E=hν. Later experiments showed that these light-quanta also matter how intense, does not initiate carry momentum and, thus, can be considered particles: the photon concept was born, the reaction. Similarly, electrons can leading to a deeper understanding of the electric and magnetic fields themselves. be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[16][17]

At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers culminated in Max Planck's hypothesis[] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E=hν. As shown by Albert Einstein, some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[18]

Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself. Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space. In 1909[] and 1916,[19] Einstein showed that, if Planck's law of black-body radiation is accepted, the energy quanta Photon 57

must also carry momentum p=h/λ, making them full-fledged particles. This photon momentum was observed experimentally by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life, and was solved in quantum electrodynamics and its successor, the Standard Model (see Second quantization and The photon as a gauge boson, below).

Early objections

Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture. However, before Compton's experiment showing that photons carried momentum proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien, Planck and Millikan.). Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, Up to 1923, most physicists were reluctant to accept that light itself where it was much more difficult not to ascribe was quantized. Instead, they tried to explain photon behavior by quantization to light itself to explain the observed quantizing only matter, as in the Bohr model of the hydrogen atom results. (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they Even after Compton's experiment, Niels Bohr, Hendrik led to quantum mechanics. Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.[20] To account for the data then available, two drastic hypotheses had to be made: 1. Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation. 2. Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a "virtual" electromagnetic field. However, refined Compton experiments showed that energy-momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible". Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics. A few physicists persisted in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photon-correlation experiments.[21] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven. Photon 58

Wave–particle duality and uncertainty principles Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution but behaves according to Maxwell's equations. However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter. Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below). A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope. The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

where is the aperture angle of the microscope. Thus, the position uncertainty can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" from the light scattering from it into the microscope. If light were not quantized into Heisenberg's thought experiment for locating an photons, the uncertainty could be made arbitrarily small by electron (shown in blue) with a high-resolution gamma-ray microscope. The incoming gamma ray reducing the light's intensity. In that case, since the wavelength (shown in green) is scattered by the electron up into the and intensity of light can be varied independently, one could microscope's aperture angle θ. The scattered gamma simultaneously determine the position and momentum to ray is shown in red. Classical optics shows that the electron position can be resolved only up to an arbitrarily high accuracy, violating the uncertainty principle. By uncertainty Δx that depends on θ and the wavelength λ contrast, Einstein's formula for photon momentum preserves the of the incoming light. uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

giving the product , which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[22] Photon 59

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase of that wave

See coherent state and squeezed coherent state for more details. Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations are simply Schrödinger's equation for photons, most physicists do not agree. For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate , and, thus, the normal Heisenberg uncertainty principle does not pertain to photons. A few substitute wave functions have been suggested for the photon, but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

Bose–Einstein model of a photon gas In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather a modification of coarse-grained counting of phase space. Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995. It was later used by Lene Hau to slow, and then completely stop, light in 1999 and 2001. The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi-Dirac statistics).

Stimulated and spontaneous emission Photon 60

In 1916, Einstein showed that Planck's radiation law could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in interaction with atoms. Consider a his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired cavity in thermal equilibrium and filled further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics. with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density of photons with frequency (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.

Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate for a system to absorb a photon of frequency and transition from a lower energy to a higher energy is proportional to the number of atoms with energy and to the energy density of ambient photons with that frequency,

where is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. Following Einstein's approach, the corresponding rate for the emission of photons of frequency and transition from a higher energy to a lower energy is

where is the rate constant for emitting a photon spontaneously, and is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates and must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of and is where are the degeneracy of the state i and that of j, respectively, their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that and

The A and Bs are collectively known as the Einstein coefficients.[23] Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients , and once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[24] In fact, in 1926, Paul Dirac derived the rate constants in using a semiclassical approach, and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory. Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory; earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field. Photon 61

Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow. Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function was inspired by Einstein's later work searching for a more complete theory.[25]

Second quantization

In 1910, Peter Debye derived Planck's law of black-body radiation from a relatively simple assumption. He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of , where is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.

In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way. As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and

polarization state—are equivalent to a set of uncoupled simple Different electromagnetic modes (such as those harmonic oscillators. Treated quantum mechanically, the energy depicted here) can be treated as independent simple levels of such oscillators are known to be , where is harmonic oscillators. A photon corresponds to a unit of energy E=hν in its electromagnetic mode. the oscillator frequency. The key new step was to identify an electromagnetic mode with energy as a state with photons, each of energy . This approach gives the correct energy fluctuation formula. Photon 62

Dirac took this one step further. He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's and coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of black body radiation by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics. Dirac's second-order perturbation theory can involve virtual photons, In quantum field theory, the probability of an event is computed by summing the probability transient intermediate states of the electromagnetic field; the static amplitude (a complex number) for all possible electric and magnetic interactions are mediated by such virtual ways in which the event can occur, as in the photons. In such quantum field theories, the probability amplitude of Feynman diagram shown here; the probability observable events is calculated by summing over all possible equals the square of the modulus of the total amplitude. intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy , and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such second-order and higher-order perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization. Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron-positron pairs.[26] In fact, such photon-photon scattering, as well as electron-photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.

In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode

where represents the state in which photons are in the mode . In this notation, the creation of a new photon in mode (e.g., emitted from an atomic transition) is written as . This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

The hadronic properties of the photon Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[27] in spite of the fact that the electric charge structures of protons and neutrons are substantially different. A theory called Vector Meson Dominance (VMD) was developed to explain this effect. According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.[28] However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasi-free according to asymptotic freedom in QCD and described by the photon structure function.[29][30] A comprehensive comparison of data with theoretical predictions is presented in a recent review.[31] Photon 63

The photon as a gauge boson The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime. For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of a complex number, which reflects the ability to vary the phase of a complex number without affecting observables or real valued functions made from it, such as the energy or the Lagrangian. The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be . These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states. In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W− and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[32][33][34] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.[35]

Contributions to the mass of a system The energy of a system that emits a photon is decreased by the energy of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount . Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[36] This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[37] Since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound-Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[38]

Photons in matter Any 'explanation' of how photons travel through matter has to explain why different arrangements of matter are transparent or opaque at different wavelengths (light through carbon as diamond or not, as graphite) and why individual photons behave in the same way as large groups. Explanations that invoke 'absorption' and 're-emission' have to provide an explanation for the directionality of the photons (diffraction, reflection) and further explain how entangled photon pairs can travel through matter without their quantum state collapsing. The simplest explanation is that light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. Photon 64

An example would be in the core of the Sun. Energy can take about a million years to reach the surface. However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibrium between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitation of the matter (quasi-particles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c. Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed.[39] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed. Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.[40] Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal C H O, which is responsible for vision, as discovered in 1958 20 28 by Nobel laureate biochemist George Wald and co-workers. The absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[41][42] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration.

Technological applications Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission. Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.[43] Planck's energy formula is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum of a fluorescent light bulb can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.[44] Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy. Photon 65

In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins. Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beam-splitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".

Recent research Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[45]

Notes [1] . An English translation is available from Wikisource.

[2] Although the 1967 Elsevier translation (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1918/ planck-lecture. html) of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein

The origin and development of the quantum theory (http:/ / books. google. com/ books?id=4UC4AAAAIAAJ), The Clarendon Press, 1922

(here (http:/ / www. readanybook. com/ ebook/ the-origin-and-development-of-the-quantum-theory-48217#downloadable)) uses

"light-quantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also this note (http:/ / www. nobeliefs. com/

photon. htm)). [3] The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon?

http:/ / math. ucr. edu/ home/ baez/ physics/ ParticleAndNuclear/ photon_mass. html [4] Role as gauge boson and polarization section 5.1 in [5] See p.31 in [6] See section 1.6 in

[7] Davison E. Soper, Electromagnetic radiation is made of photons (http:/ / physics. uoregon. edu/ ~soper/ Light/ photons. html), Institute of Theoretical Science, University of Oregon [8] This property was experimentally verified by Raman and Bhagavantam in 1931: [9] E.g., section 1.3.3.2 in [10] E.g., section 9.3 in [11] E.g., Appendix XXXII in

[12] Summary Table (http:/ / pdg. lbl. gov/ 2009/ tables/ contents_tables. html)

[13] preprint (http:/ / arxiv. org/ abs/ hep-ph/ 0306245)

[14] . An English translation (http:/ / www. gutenberg. org/ etext/ 14725) is available from Project Gutenberg [15] This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society. [16] Frequency-dependence of luminiscence p. 276f., photoelectric effect section 1.4 in [17] The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). " Photon density and the

correspondence principle of electromagnetic interaction (http:/ / adsabs. harvard. edu/ abs/ 1996AIPC. . 369. 1234B)".) By comparison, sunlight is only about 0.1 W/cm2.

[18] Presentation speech by Svante Arrhenius for the 1921 Nobel Prize in Physics, December 10, 1922. Online text (http:/ / nobelprize. org/

nobel_prizes/ physics/ laureates/ 1921/ press. html) from [nobelprize.org], The Nobel Foundation 2008. Access date 2008-12-05. [19] Also Physikalische Zeitschrift, 18, 121–128 (1917). [20] Also Zeitschrift für Physik, 24, 69 (1924). Photon 66

[21] These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below under #Additional references.) [22] E.g., p. 10f. in [23] Section 1.4 in [24] P. 322 in : [25] Specifically, Born claimed to have been inspired by Einstein's never-published attempts to develop a "ghost-field" theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell's equations. [26] Photon-photon-scattering section 7-3-1, renormalization chapter 8-2 in [27] Bauer, T. H., Spital, R. D., Yennie, D. R. and Pipkin, F. M, The hadronic properties of the photon in high-energy interactions, Rev. Mod. Phys. 50, 261–436 (1978), pages 292–293 [28] Theory of strong interactions, J. J. Sakurai, Ann. Phys., 11 (1960) [29] T.F. Walsh and P.M. Zerwas, Two-photon processes in the parton model, Physics Letters B44 (1973) 195 [30] E.Witten, Anomalous cross-section for photon - photon scattering in gauge theories, Nuclear Physics B120 (1977) 189 [31] R. Nisius, The photon structure from deep inelastic electron photon scattering, Physics Report 332 (2000) 165

[32] Sheldon Glashow Nobel lecture (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1979/ glashow-lecture. html), delivered 8 December 1979.

[33] Abdus Salam Nobel lecture (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1979/ salam-lecture. html), delivered 8 December 1979.

[34] Steven Weinberg Nobel lecture (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1979/ weinberg-lecture. html), delivered 8 December 1979. [35] E.g., chapter 14 in [36] E.g., section 10.1 in [37] Radiative correction to electron mass section 7-1-2, anomalous magnetic moments section 7-2-1, Lamb shift section 7-3-2 and hyperfine splitting in positronium section 10-3 in [38] E. g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in [39] Ch 4 in [40] Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in [41] E.g., section 11-5 C in

[42] Nobel lecture given by G. Wald on December 12, 1967, online at nobelprize.org: The Molecular Basis of Visual Excitation (http:/ /

nobelprize. org/ nobel_prizes/ medicine/ laureates/ 1967/ wald-lecture. html). [43] Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in

[44] An example is US Patent Nr. 5212709 (http:/ / patft. uspto. gov/ netacgi/ nph-Parser?Sect1=PTO1& Sect2=HITOFF& d=PALL& p=1& u=/

netahtml/ PTO/ srchnum. htm& r=1& f=G& l=50& s1=5212709. PN. & OS=PN/ 5212709& RS=PN/ 5212709). [45] Introductory-level material on the various sub-fields of quantum optics can be found in

References

Additional references By date of publication: • Clauser, J.F. (1974). "Experimental distinction between the quantum and classical field-theoretic predictions for

the photoelectric effect". Physical Review D 9 (4): 853–860. Bibcode: 1974PhRvD...9..853C (http:/ / adsabs.

harvard. edu/ abs/ 1974PhRvD. . . 9. . 853C). doi: 10.1103/PhysRevD.9.853 (http:/ / dx. doi. org/ 10. 1103/

PhysRevD. 9. 853). • Kimble, H.J.; Dagenais, M.; Mandel, L. (1977). "Photon Anti-bunching in Resonance Fluorescence". Physical

Review Letters 39 (11): 691–695. Bibcode: 1977PhRvL..39..691K (http:/ / adsabs. harvard. edu/ abs/ 1977PhRvL.

. 39. . 691K). doi: 10.1103/PhysRevLett.39.691 (http:/ / dx. doi. org/ 10. 1103/ PhysRevLett. 39. 691). • Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. • Feynman, Richard (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 978-0-691-12575-6. • Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences". Europhysics Letters 1 (4): 173–179. Bibcode: Photon 67

1986EL...... 1..173G (http:/ / adsabs. harvard. edu/ abs/ 1986EL...... 1. . 173G). doi: 10.1209/0295-5075/1/4/004

(http:/ / dx. doi. org/ 10. 1209/ 0295-5075/ 1/ 4/ 004).

• Lamb, W.E. (1995). "Anti-photon". Applied Physics B 60 (2–3): 77–84. Bibcode: 1995ApPhB..60...77L (http:/ /

adsabs. harvard. edu/ abs/ 1995ApPhB. . 60. . . 77L). doi: 10.1007/BF01135846 (http:/ / dx. doi. org/ 10. 1007/ BF01135846).

• Special supplemental issue of Optics and Photonics News (vol. 14, October 2003) article web link (http:/ / www.

sheffield. ac. uk/ polopoly_fs/ 1. 14183!/ file/ photon. pdf) • Roychoudhuri, C.; Rajarshi, R. (2003). "The nature of light: what is a photon?". Optics and Photonics News 14: S1 (Supplement). • Zajonc, A. "Light reconsidered". Optics and Photonics News 14: S2–S5 (Supplement). • Loudon, R. "What is a photon?". Optics and Photonics News 14: S6–S11 (Supplement). • Finkelstein, D. "What is a photon?". Optics and Photonics News 14: S12–S17 (Supplement). • Muthukrishnan, A.; Scully, M.O.; Zubairy, M.S. "The concept of the photon—revisited". Optics and Photonics News 14: S18–S27 (Supplement). • Mack, H.; Schleich, W.P.. "A photon viewed from Wigner phase space". Optics and Photonics News 14: S28–S35 (Supplement).

• Glauber, R. (2005). "One Hundred Years of Light Quanta" (http:/ / nobelprize. org/ nobel_prizes/ physics/

laureates/ 2005/ glauber-lecture. pdf). 2005 Physics Nobel Prize Lecture. Education with single photons: • Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). "Observing the quantum

behavior of light in an undergraduate laboratory" (http:/ / people. whitman. edu/ ~beckmk/ QM/ grangier/

Thorn_ajp. pdf). American Journal of Physics 72 (9): 1210–1219. Bibcode: 2004AmJPh..72.1210T (http:/ /

adsabs. harvard. edu/ abs/ 2004AmJPh. . 72. 1210T). doi: 10.1119/1.1737397 (http:/ / dx. doi. org/ 10. 1119/ 1. 1737397). • Bronner, P.; et al., Andreas; Silberhorn, Christine; Meyn, Jan-Peter (2009). "Interactive screen experiments with

single photons" (http:/ / www. QuantumLab. de). European Journal of Physics 30 (2): 345–353. Bibcode:

2009EJPh...30..345B (http:/ / adsabs. harvard. edu/ abs/ 2009EJPh. . . 30. . 345B). doi:

10.1088/0143-0807/30/2/014 (http:/ / dx. doi. org/ 10. 1088/ 0143-0807/ 30/ 2/ 014). Physics 68 Physics

Various examples of physical phenomena

Part of a series on Science

• Outline • Portal • Category

Physics (from Greek φυσική (ἐπιστήμη), i.e. "knowledge of nature", from φύσις, physis, i.e. "nature") is the natural science that involves the study of matter[1] and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.[2] Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy.[3] Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right.[4] Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus. Physics 69

History

Natural philosophy has its origins in Greece during the Archaic period, (650 BCE – 480 BCE), when Pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause.[5] They proposed ideas verified by reason and observation and many of their hypotheses proved successful in experiment, for example atomism.

Classical physics became a separate science when early modern Europeans used these experimental and quantitative methods to discover what are now considered to be the laws of physics.[6] Kepler, Galileo and more specifically Newton discovered and unified the different laws of motion.[7] During the industrial revolution, as energy needs increased, so did research, which led to the

Sir Isaac Newton (1643–1727) discovery of new laws in thermodynamics, chemistry and electromagnetics. Modern physics started with the works of Max Planck in quantum theory and Einstein in relativity, and continued in quantum mechanics pioneered by Heisenberg, Schrödinger and Paul Dirac.

Philosophy

In many ways, physics stems from ancient Greek philosophy. From Thales' first attempt to characterize matter, to Democritus' deduction that matter ought to reduce to an invariant state, the Ptolemaic astronomy of a crystalline firmament, and Aristotle's book Physics (an early book on physics, which attempted to analyze and define motion from a philosophical point of view), various Greek philosophers advanced their own theories of nature. Physics was known as

Albert Einstein (1879–1955) natural philosophy until the late 18th century. By the 19th century physics was realized as a discipline distinct from philosophy and the other sciences. Physics, as with the rest of science, relies on philosophy of science to give an adequate description of the scientific method.[8] The scientific method employs a priori reasoning as well as a posteriori reasoning and the use of Bayesian inference to measure the validity of a given theory.[9] The development of physics has answered many questions of early philosophers, but has also raised new questions. Study of the philosophical issues surrounding physics, the philosophy of physics, involves issues such as the nature of space and time, determinism, and metaphysical outlooks such as empiricism, naturalism and realism.[10] Many physicists have written about the philosophical implications of their work, for instance Laplace, who championed causal determinism,[11] and Erwin Schrödinger, who wrote on quantum mechanics.[12] The mathematical physicist Roger Penrose has been called a Platonist by Stephen Hawking,[13] a view Penrose discusses in his book, The Road to Reality.[14] Hawking refers to himself as an "unashamed reductionist" and takes issue with Penrose's views. Physics 70

Core theories Though physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity). For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727). These central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.

Classical physics

Classical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism. Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics. Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics. Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which

exhibit all of the phenomena of visible light except visibility, e.g., Classical physics implemented in an acoustic reflection, refraction, interference, diffraction, dispersion, and engineering model of sound reflecting from an polarization of light. Heat is a form of energy, the internal energy acoustic diffuser possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy. Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest. Physics 71

Modern physics

Modern physics

Schrödinger equation

History of modern physics

Classical physics is generally concerned with matter and energy on the normal scale of observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on a very large or very small scale. For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified. The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary Solvay Conference of 1927, with prominent physicists such as Albert Einstein, Werner to produce many types of particles in large particle accelerators. On Heisenberg, Max Planck, Hendrik Lorentz, Niels this scale, ordinary, commonsense notions of space, time, matter, and Bohr, Marie Curie, Erwin Schrödinger and Paul energy are no longer valid. Dirac. The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics. Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena. The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation. Both quantum theory and the theory of relativity find applications in all areas of modern physics.

Difference between classical and modern physics

While physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match The basic domains of physics their predictions. Albert Einstein contributed the framework of special relativity, which replaced notions of absolute time and space with spacetime and allowed an accurate description of systems whose components have speeds approaching the speed of light. Max

Planck, Erwin Schrödinger, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales. Later, quantum field theory unified Physics 72

quantum mechanics and special relativity. General relativity allowed for a dynamical, curved spacetime, with which highly massive systems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.

Relation to other fields

Prerequisites

Mathematics is the language used for compact description of the order in nature, especially the laws of physics. This was noted and advocated by Pythagoras, Plato, Galileo,[15] and Newton. Physics theories use mathematics to obtain order and provide precise formulas, precise or estimated solutions, quantitative results and predictions. Experiment results in physics are numerical measurements. Technologies based on mathematics, like computation This parabola-shaped lava flow illustrates the have made computational physics an active area of research. application of mathematics in physics—in this case, Galileo's law of falling bodies.

Mathematics and ontology are used in physics. Physics is used in chemistry and cosmology. Physics 73

Ontology is a prerequisite for physics, but not for mathematics. It means physics is ultimately concerned with descriptions of the real world, while mathematics is concerned with abstract patterns, even beyond the real world. Thus physics statements are synthetic, while math statements are analytic. Mathematics contains hypotheses, while physics contains theories. Mathematics statements have to be only logically true, while predictions of physics statements must match observed and experimental data.

The distinction is clear-cut, but not always obvious. For example, The distinction between mathematics and physics mathematical physics is the application of mathematics in physics. Its is clear-cut, but not always obvious, especially in methods are mathematical, but its subject is physical.[16] The problems mathematical physics. in this field start with a "math model of a physical situation" and a "math description of a physical law". Every math statement used for solution has a hard-to-find physical meaning. The final mathematical solution has an easier-to-find meaning, because it is what the solver is looking for.

Physics is a branch of fundamental science, not practical science.[17] Physics is also called "the fundamental science" because the subject of study of all branches of natural science like chemistry, astronomy, geology and biology are constrained by laws of physics. For example, chemistry studies properties, structures, and reactions of matter (chemistry's focus on the atomic scale distinguishes it from physics). Structures are formed because particles exert electrical forces on each other, properties include physical characteristics of given substances, and reactions are bound by laws of physics, like conservation of energy, mass and charge. Physics is applied in industries like engineering and medicine.

Application and influence

Applied physics is a general term for physics research which is intended for a particular use. An applied physics curriculum usually contains a few classes in an applied discipline, like geology or electrical engineering. It usually differs from engineering in that an applied physicist may not be designing something in particular, but rather is using physics or conducting physics research with the aim of developing new technologies or solving a problem.

The approach is similar to that of applied mathematics. Applied physicists can also be interested in the use of physics for scientific research. For instance, Archimedes' screw, a simple machine for lifting people working on accelerator physics might seek to build better particle detectors for research in theoretical physics. Physics is used heavily in engineering. For example, statics, a subfield of mechanics, is used in the building of bridges and other static structures. The understanding and use of acoustics results in sound control and better concert halls; similarly, the use of optics creates better optical devices. An understanding of physics makes for more realistic flight simulators, video games, and movies, and is often critical in forensic investigations. With the standard consensus that the laws of physics are universal and do not change with time, physics can be used to study things that would ordinarily be mired in uncertainty. For example, in the study of the origin of the earth, one can reasonably model earth's mass, temperature, and rate of rotation, as a Physics 74

function of time allowing one to extrapolate forward and backward in time and so predict prior and future conditions. It also allows for simulations in engineering which drastically speed up the development of a new technology. But there is also considerable interdisciplinarity in the physicist's methods and so many other important fields are influenced by physics, e.g. the fields of econophysics and sociophysics.

The application of physical laws in lifting liquids

Research

Scientific method Physicists use the scientific method to test the validity of a physical theory, using a methodical approach to compare the implications of the theory in question with the associated conclusions drawn from experiments and observations conducted to test it. Experiments and observations are collected and compared with the predictions and hypotheses made by a theory, thus aiding in the determination or the validity/invalidity of the theory. A scientific law is a concise verbal or mathematical statement of a relation that expresses a fundamental principle of a theory, like Newton's law of universal gravitation.

Theory and experiment

Theorists seek to develop mathematical models that both agree with existing experiments and successfully predict future experimental results, while experimentalists devise and perform experiments to test theoretical predictions and explore new phenomena. Although theory and experiment are developed separately, they are strongly dependent upon each other. Progress in physics frequently comes about when experimentalists make a discovery that existing theories cannot explain, or when new theories generate experimentally testable predictions, which inspire new experiments.

Physicists who work at the interplay of theory and experiment are called phenomenologists. Phenomenologists look at the complex phenomena observed in experiment and work to relate them to The astronaut and Earth are both in free-fall fundamental theory. Theoretical physics has historically taken inspiration from philosophy; electromagnetism was unified this way.[18] Beyond the known Physics 75

universe, the field of theoretical physics also deals with hypothetical issues,[19] such as parallel universes, a multiverse, and higher dimensions. Theorists invoke these ideas in hopes of solving particular problems with existing theories. They then explore the consequences of these ideas and work toward making testable predictions. Experimental physics expands, and is expanded by, engineering and technology. Experimental physicists involved in basic research design and perform experiments with equipment such as particle accelerators and lasers, whereas those involved in applied research often work in industry, developing technologies such as magnetic resonance imaging Lightning is an electric current (MRI) and transistors. Feynman has noted that experimentalists may seek areas which are not well-explored by theorists.[20]

Scope and aims

Physics covers a wide range of phenomena, from elementary particles (such as quarks, neutrinos and electrons) to the largest superclusters of galaxies. Included in these phenomena are the most basic objects composing all other things. Therefore physics is sometimes called the "fundamental science".[] Physics aims to describe the various phenomena that occur in nature in terms of simpler phenomena. Thus, physics aims to both connect the things observable to humans to root causes, and then connect these causes together.

For example, the ancient Chinese observed that certain rocks (lodestone) were attracted to one another by some invisible force. This Physics involves modeling the natural world with effect was later called magnetism, and was first rigorously studied in theory, usually quantitative. Here, the path of a the 17th century. A little earlier than the Chinese, the ancient Greeks particle is modeled with the mathematics of calculus to explain its behavior: the purview of knew of other objects such as amber, that when rubbed with fur would the branch of physics known as mechanics. cause a similar invisible attraction between the two. This was also first studied rigorously in the 17th century, and came to be called electricity. Thus, physics had come to understand two observations of nature in terms of some root cause (electricity and magnetism). However, further work in the 19th century revealed that these two forces were just two different aspects of one force—electromagnetism. This process of "unifying" forces continues today, and electromagnetism and the weak nuclear force are now considered to be two aspects of the electroweak interaction. Physics hopes to find an ultimate reason (Theory of Everything) for why nature is as it is (see section Current research below for more information).

Research fields Contemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education. Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968), who worked in multiple fields of physics, are now very rare.[21] Physics 76

Condensed matter

Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.

The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phases include the superfluid and the phase of matter, the Bose–Einstein condensate Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials, and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.

Condensed matter physics is by far the largest field of contemporary physics. Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics. Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.

Atomic, molecular, and optical physics Atomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view). Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions,[citation needed] low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics. Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light. Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm. Physics 77

High-energy physics (particle physics) and nuclear physics

Particle physics is the study of the elementary constituents of matter and energy, and the interactions between them. In addition, particle physicists design and develop the high energy accelerators, detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.

Currently, the interactions of elementary particles and fields are described by the Standard Model. The model accounts for the 12 known particles of matter (quarks and leptons) that interact via the

strong, weak, and electromagnetic fundamental forces. Dynamics are A simulated event in the CMS detector of the described in terms of matter particles exchanging gauge bosons Large Hadron Collider, featuring a possible (gluons, W and Z bosons, and photons, respectively). The Standard appearance of the Higgs boson. Model also predicts a particle known as the Higgs boson, the existence of which has not yet been verified. In July 2012 CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.

Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.

Astrophysics

Astrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.

The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere The deepest visible-light image of the universe, make space-based observations necessary for infrared, ultraviolet, the Hubble Ultra Deep Field gamma-ray, and X-ray astronomy.

Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang. The Big Bang was confirmed by the success of Big Bang nucleosynthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle. Cosmologists have recently established the ΛCDM model of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter. Physics 78

Numerous possibilities and discoveries are anticipated to emerge from new data from the Fermi Gamma-ray Space Telescope over the upcoming decade and vastly revise or clarify existing models of the universe.[22] In particular, the potential for a tremendous discovery surrounding dark matter is possible over the next several years. Fermi will search for evidence that dark matter is composed of weakly interacting massive particles, complementing similar experiments with the Large Hadron Collider and other underground detectors. IBEX is already yielding new astrophysical discoveries: "No one knows what is creating the ENA (energetic neutral atoms) ribbon" along the termination shock of the solar wind, "but everyone agrees that it means the textbook picture of the heliosphere — in which the solar system's enveloping pocket filled with the solar wind's charged particles is plowing through the onrushing 'galactic wind' of the interstellar medium in the shape of a comet — is wrong."

Current research

Research in physics is continually progressing on a large number of fronts. In condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers. In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These Feynman diagram signed by R.P. Feynman experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the Higgs boson and supersymmetric particles.[23]

Theoretical attempts to unify quantum mechanics and general relativity into a single theory of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current

leading candidates are M-theory, superstring theory and loop quantum A typical event described by physics: a magnet gravity. levitating above a superconductor demonstrates the Meissner effect. Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies. Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood.[citation needed] Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sandpiles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.[citation needed] These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems. In 1932, Horace Lamb said: Physics 79

I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.

References [1] Richard Feynman begins his Lectures with the atomic hypothesis, as his most compact statement of all scientific knowledge: "If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations ..., what statement would contain the most information in the fewest words? I believe it is ... that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. ..." [2] Note: The term 'universe' is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and constants that govern them. However, the term 'universe' may also be used in slightly different contextual senses, denoting concepts such as the cosmos or the philosophical world. [3] The earliest civilizations dating back to beyond 3000 BCE, such as the Sumerians, Ancient Egyptians, and the Indus Valley Civilization, all had a predictive knowledge and a very basic understanding of the motions of the Sun, Moon, and stars. [4] Francis Bacon's 1620 Novum Organum was critical in the development of scientific method. [5] Singer, C. A Short History of Science to the 19th century. Streeter Press, 2008. p. 35. [6] Weidhorn Introduces Galili as the "father of modern Physics" [7] Guicciardini, Niccolò (1999), Reading the Principia: The Debate on Newton's Methods for Natural Philosophy from 1687 to 1736, New York: Cambridge University Press. [8] See Chapter 1 for a discussion on the necessity of philosophy of science. [9] Peter Godfrey-Smith (2003), Chapter 14 "Bayesianism and Modern Theories of Evidence" Theory and Reality: an introduction to the philosophy of science ISBN 0-226-30063-3 [10] Peter Godfrey-Smith (2003), Chapter 15 "Empiricism, Naturalism, and Scientific Realism?" Theory and Reality: an introduction to the philosophy of science ISBN 0-226-30063-3 [11] See Laplace, Pierre Simon, A Philosophical Essay on Probabilities, translated from the 6th French edition by Frederick Wilson Truscott and Frederick Lincoln Emory, Dover Publications (New York, 1951) [12] See "The Interpretation of Quantum Mechanics" Ox Bow Press (1995) ISBN 1-881987-09-4. and "My View of the World" Ox Bow Press (1983) ISBN 0-918024-30-7. [13] Stephen Hawking and Roger Penrose (1996), The Nature of Space and Time ISBN 0-691-05084-8 p.4 "I think that Roger is a Platonist at heart but he must answer for himself." [14] Roger Penrose, The Road to Reality ISBN 0-679-45443-8 [15] "Philosophy is written in that great book which ever lies before our eyes. I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth." – Galileo (1623), The Assayer, as quoted by G. Toraldo Di Francia (1976), The Investigation of the Physical World ISBN 0-521-29925-X p.10 [16] The application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for

the formulation of physical theories." Definition from the Journal of Mathematical Physics. http:/ / jmp. aip. org/ jmp/ staff. jsp [17] American Association for the Advancement of Science, Science. 1917. Page 645 [18] See, for example, the influence of Kant and Ritter on Oersted. [19] Concepts which are denoted hypothetical can change with time. For example, the atom of nineteenth century physics was denigrated by some, including Ernst Mach's critique of Ludwig Boltzmann's formulation of statistical mechanics. By the end of World War II, the atom was no longer deemed hypothetical. [20] p.157: "In fact experimenters have a certain individual character. They ... very often do their experiments in a region in which people know the theorist has not made any guesses. " [21] Yet, universalism is encouraged in the culture of physics. For example, the World Wide Web, which was innovated at CERN by Tim Berners-Lee, was created in service to the computer infrastructure of CERN, and was/is intended for use by physicists worldwide. The same might be said for arXiv.org

[22] See also Nasa - Fermi Science (http:/ / www. nasa. gov/ mission_pages/ GLAST/ science/ index. html) and NASA - Scientists Predict Major

Discoveries for GLAST (http:/ / www. nasa. gov/ mission_pages/ GLAST/ science/ unidentified_sources. html). [23] 584 co-authors "Direct observation of the strange 'b' baryon UNIQ-math-0-19b700d988ba3161-QINU " Fermilab-Pub-07/196-E, 12 June

2007 http:/ / arxiv. org/ abs/ 0706. 1690v2 finds a mass of 5.774 GeV for the UNIQ-math-1-19b700d988ba3161-QINU Physics 80

External links General

• Encyclopedia of Physics (http:/ / www. scholarpedia. org/ article/ Encyclopedia_of_physics) at Scholarpedia

• de Haas, Paul, "Historic Papers in Physics (20th Century)" (http:/ / home. tiscali. nl/ physis/ HistoricPaper/ )Wikipedia:Link rot

• PhysicsCentral (http:/ / www. physicscentral. com/ ) – Web portal run by the American Physical Society (http:/ /

www. aps. org/ )

• Physics.org (http:/ / www. physics. org/ ) – Web portal run by the Institute of Physics (http:/ / www. iop. org/ )

• The Skeptic's Guide to Physics (http:/ / musr. physics. ubc. ca/ ~jess/ hr/ skept/ )

• Usenet Physics FAQ (http:/ / math. ucr. edu/ home/ baez/ physics/ ) – A FAQ compiled by sci.physics and other physics newsgroups

• Website of the Nobel Prize in physics (http:/ / nobelprize. org/ nobel_prizes/ physics/ )

• World of Physics (http:/ / scienceworld. wolfram. com/ physics/ ) An online encyclopedic dictionary of physics

• Nature: Physics (http:/ / www. nature. com/ naturephysics)

• Physics (http:/ / physics. aps. org/ ) announced 17 July 2008 by the American Physical Society

• Physics/Publications (http:/ / www. dmoz. org/ / Science/ Physics/ Publications/ / ) at the Open Directory Project

• Physicsworld.com (http:/ / physicsworld. com/ ) – News website from Institute of Physics Publishing (http:/ /

publishing. iop. org/ )

• Physics Central (http:/ / physlib. com/ ) – includes articles on astronomy, particle physics, and mathematics.

• The Vega Science Trust (http:/ / www. vega. org. uk/ ) – science videos, including physics

• Video: Physics "Lightning" Tour with Justin Morgan (http:/ / www. archive. org/ details/

JustinMorganPhysicsLightningTour/ )

• 52-part video course: The Mechanical Universe...and Beyond (http:/ / www. learner. org/ resources/ series42.

html) Note: also available at - Introduction Physics (https:/ / video. google. com/ videoplay?docid=01) at Google Videos (Adobe Flash video)

• HyperPhysics website (http:/ / hyperphysics. phy-astr. gsu. edu/ Hbase/ hframe. html) – HyperPhysics, a physics and astronomy mind-map from Georgia State University Organizations

• AIP.org (http:/ / www. aip. org/ index. html) – Website of the American Institute of Physics

• APS.org (http:/ / www. aps. org/ ) – Website of the American Physical Society

• IOP.org (http:/ / www. iop. org/ ) – Website of the Institute of Physics

• PlanetPhysics.org (http:/ / planetphysics. org/ )

• Royal Society (http:/ / www. royalsoc. ac. uk/ ) – Although not exclusively a physics institution, it has a strong history of physics

• SPS National (http:/ / www. spsnational. org/ ) – Website of the Society of Physics Students Quantum mechanics 81 Quantum mechanics

Quantum mechanics Introduction Glossary · History

Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant. It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It is the non-relativistic limit of Quantum Field Theory (QFT), a theory that was developed later that combined Quantum Mechanics with Relativity. In advanced topics of quantum mechanics, some of these behaviors are macroscopic (see macroscopic quantum phenomena) and emerge at only extreme (i.e., very low or very high) energies or temperatures (such as in the use of superconducting magnets). The name quantum mechanics derives from the observation that some physical quantities can change only in discrete amounts (Latin quanta), and not in a continuous (cf. analog) way. For example, the angular momentum of an electron bound to an atom or molecule is quantized.[1] In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects. The mathematical formulations of quantum mechanics are abstract. A mathematical function known as the wavefunction provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator, and the mathematics is akin to that describing acoustic resonance. Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics—for instance, the ground state in a quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, as opposed to a more "traditional" system that is thought of as simply being at rest, with zero kinetic energy. Instead of a traditional static, unchanging zero state, quantum mechanics allows for far more dynamic, chaotic possibilities, according to John Wheeler. The earliest versions of quantum mechanics were formulated in the first decade of the 20th century. At around the same time, the atomic theory and the corpuscular theory of light (as updated by Einstein) first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively. Early quantum theory was significantly reformulated in the mid-1920s by Werner Heisenberg, Max Born and Pascual Jordan, who created matrix mechanics; Louis de Broglie and Erwin Schrödinger (Wave Mechanics); and Wolfgang Pauli and Satyendra Nath Bose (statistics of subatomic particles). Moreover, the Copenhagen interpretation of Niels Bohr became widely accepted. By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann, with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality, and philosophical speculation about the role of the observer. Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines, such as quantum chemistry, quantum electronics, quantum optics, and quantum information science. Much 19th century physics has been re-evaluated as the "classical limit" of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories. Quantum mechanics 82

History

Modern physics

Schrödinger equation

History of modern physics

Scientific inquiry into the wave nature of light began in the 17th and 18th centuries when scientists such as Robert Hooke, Christian Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations.[2] In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he later described in a paper entitled "On the nature of light and colours". This experiment played a major role in the general acceptance of the wave theory of light. In 1838, with the discovery of cathode rays by Michael Faraday, these studies were followed by the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, and the 1900 quantum hypothesis of Max Planck. Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" (or "energy elements") precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it was valid only at high frequencies, and underestimated the radiance at low frequencies. Later, Max Planck corrected this model using Boltzmann statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics. Among the first to study quantum phenomena in nature were Arthur Compton, C.V. Raman, Pieter Zeeman, each of whom has a quantum effect named after him. Robert A. Millikan studied the Photoelectric effect experimentally and Albert Einstein developed a theory for it. At the same time Niels Bohr developed his theory of the atomic structure which was later confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept also introduced by Arnold Sommerfeld.[3] This phase is known as Old quantum theory. According to Planck, each energy element E is proportional to its frequency ν: Quantum mechanics 83

where h is Planck's constant. Planck (cautiously) insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizeable discovery. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material.

Planck is considered the father of the Quantum Theory

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld and others. In the mid-1920s, developments in quantum mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that The 1927 Solvay Conference in Brussels. closed the "Old Quantum Theory". Out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons (1926). From Einstein's simple postulation was born a flurry of debating, theorizing, and testing. Thus the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves, such as visible and ultraviolet light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or "quanta", Albert Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle (later called the photon) with a discrete quantum of energy that was dependent on its frequency.[4] As a matter of fact, Einstein was able to use the photon theory of light to explain the photoelectric effect, for which he won the Nobel Prize in 1921. This led to a theory of unity between subatomic particles and electromagnetic waves, called wave–particle duality, in which particles and waves were neither one nor the other, but had certain properties of both. Thus coined the term wave-particle duality. While quantum mechanics traditionally described the world of the very small, it is also needed to explain certain recently investigated macroscopic systems such as superconductors, superfluids, and larger organic molecules. The word quantum derives from the Latin, meaning "how great" or "how much". In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1). The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and sub-atomic systems which is today called quantum mechanics. It is the underlying Quantum mechanics 84

mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics.[5] Some fundamental aspects of the theory are still actively studied.[6] Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller. If classical mechanics alone governed the workings of an atom, electrons could not really "orbit" the nucleus. Since bodies in circular motion are accelerating, electrons must emit radiation, losing energy and eventually colliding with the nucleus in the process. This clearly contradicts the existence of stable atoms. However, in the natural world, electrons normally remain in an uncertain, non-deterministic, "smeared", probabilistic, wave–particle wavefunction orbital path around (or through) the nucleus, defying the traditional assumptions of classical mechanics and electromagnetism. Quantum mechanics was initially developed to provide a better explanation and description of the atom, especially the differences in the spectra of light emitted by different isotopes of the same element, as well as subatomic particles. In short, the quantum-mechanical atomic model has succeeded spectacularly in the realm where classical mechanics and electromagnetism falter. Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: • The quantization of certain physical properties • Wave–particle duality • The uncertainty principle • Quantum entanglement.

Mathematical formulations In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac,[7] David Hilbert,[8] John von Neumann,[9] and Hermann Weyl[10] the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space - variously called the "state space" or the "associated Hilbert space" of the system - that is well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system - for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can attain only those discrete eigenvalues. In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.[11] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be considered (to a certain probability) to be located somewhere within a given region of space, but with their exact positions unknown. Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate momentum. Quantum mechanics 85

According to one interpretation, as the result of a measurement the wave function containing the probability information for a system collapses from a given initial state to a particular eigenstate. The possible results of a measurement are the eigenvalues of the operator representing the observable — which explains the choice of Hermitian operators, for which all the eigenvalues are real. The probability distribution of an observable in a given state can be found by computing the spectral decomposition of the corresponding operator. Heisenberg's uncertainty principle is represented by the statement that the operators corresponding to certain observables do not commute. The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr-Einstein debates, in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been extensively studied. Newer interpretations of quantum mechanics have been formulated that do away with the concept of "wavefunction collapse" (see, for example, the relative state interpretation). The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum mechanics.[12] Generally, quantum mechanics does not assign definite values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining the possible outcomes from measuring an observable. Often these results are skewed by many causes, such as dense probability clouds. Probability clouds are approximate, but better than the Bohr model, whereby electron location is given by a probability function, the wave function eigenvalue, such that the probability is the squared modulus of the complex amplitude, or quantum state nuclear attraction.[13] Naturally, these probabilities will depend on the quantum state at the "instant" of the measurement. Hence, uncertainty is involved in the value. There are, however, certain states that are associated with a definite value of a particular observable. These are known as eigenstates of the observable ("eigen" can be translated from German as meaning "inherent" or "characteristic").[14] In the everyday world, it is natural and intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum (since they are conjugate pairs) or its energy and time (since they too are conjugate pairs); rather, it provides only a range of probabilities in which that particle might be given its momentum and momentum probability. Therefore, it is helpful to use different words to describe states having uncertain values and states having definite values (eigenstates). Usually, a system will not be in an eigenstate of the observable (particle) we are interested in. However, if one measures the observable, the wavefunction will instantaneously be an eigenstate (or "generalized" eigenstate) of that observable. This process is known as wavefunction collapse, a controversial and much-debated process that involves expanding the system under study to include the measurement device. If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wavefunction collapsing into each of the possible eigenstates. For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x (neither an 0 eigenstate of position nor of momentum). When one measures the position of the particle, it is impossible to predict with certainty the result. It is probable, but not certain, that it will be near x , where the amplitude of the wave 0 function is large. After the measurement is performed, having obtained some result x, the wave function collapses into a position eigenstate centered at x. The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (the operator corresponding to the total energy of the system) generates the time evolution. The time evolution of wave functions is deterministic in the sense that - given a wavefunction at an initial time - it makes a definite prediction of what the wavefunction will be at any later time. Quantum mechanics 86

During a measurement, on the other hand, the change of the initial wavefunction into another, later wavefunction is not deterministic, it is unpredictable (i.e., random). A time-evolution simulation can be seen here. Wave functions change as time progresses. The Schrödinger equation describes how wavefunctions change in time, playing a role similar to Newton's second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.[15] Some wave functions produce probability distributions that are constant, or independent of time - such as when in a stationary state of constant energy, time vanishes in the absolute square of the wave function. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus (Fig. 1) (note, however, that only the lowest angular momentum states, labeled s, are spherically symmetric).

The Schrödinger equation acts on the entire probability amplitude, not merely its absolute Fig. 1: Probability densities corresponding to the wavefunctions of an value. Whereas the absolute value of the electron in a hydrogen atom possessing definite energy levels (increasing probability amplitude encodes information about from the top of the image to the bottom: n = 1, 2, 3, ...) and angular probabilities, its phase encodes information about momenta (increasing across from left to right: s, p, d, ...). Brighter areas correspond to higher probability density in a position measurement. Such the interference between quantum states. This wavefunctions are directly comparable to Chladni's figures of acoustic gives rise to the "wave-like" behavior of quantum modes of vibration in classical physics, and are modes of oscillation as well, states. As it turns out, analytic solutions of the possessing a sharp energy and, thus, a definite frequency. The angular Schrödinger equation are available for only a very momentum and energy are quantized, and take only discrete values like those shown (as is the case for resonant frequencies in acoustics) small number of relatively simple model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion, and the hydrogen atom are the most important representatives. Even the helium atom - which contains just one more electron than does the hydrogen atom - has defied all attempts at a fully analytic treatment.

There exist several techniques for generating approximate solutions, however. In the important method known as perturbation theory, one uses the analytic result for a simple quantum mechanical model to generate a result for a more complicated model that is related to the simpler model by (for one example) the addition of a weak potential energy. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces only weak (small) deviations from classical behavior. These deviations can then be computed based on the classical motion. This approach is particularly important in the field of quantum chaos. Quantum mechanics 87

Mathematically equivalent formulations of quantum mechanics There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the "transformation theory" proposed by the late Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics—matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger).[16] Especially since Werner Heisenberg was awarded the Nobel Prize in Physics in 1932 for the creation of quantum mechanics, the role of Max Born in the development of QM was overlooked until the 1954 Nobel award. The role is noted in a 2005 biography of Born, which recounts his role in the matrix formulation of quantum mechanics, and the use of probability amplitudes. Heisenberg himself acknowledges having learned matrices from Born, as published in a 1940 festschrift honoring Max Planck.[17] In the matrix formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom).[18] An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible histories between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics.

Interactions with other scientific theories The rules of quantum mechanics are fundamental. They assert that the state space of a system is a Hilbert space, and that observables of that system are Hermitian operators acting on that space—although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or—equivalently—larger quantum numbers, i.e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero. In other words, classical mechanics is simply a quantum mechanics of large systems. This "high energy" limit is known as the classical or correspondence limit. One can even start from an established classical model of a particular system, then attempt to guess the underlying quantum model that would give rise to the classical model in the correspondence limit.

List of unsolved problems in physics

In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantum description of reality, which includes elements such as the "superposition of states" and "wavefunction collapse", give rise to the reality we perceive?

When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator. Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein-Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been employed since the inception of quantum mechanics, Quantum mechanics 88

is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles. Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work. It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity (the most accurate theory of gravity currently known) and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity. Classical mechanics has also been extended into the complex domain, with complex classical mechanics exhibiting behaviors similar to quantum mechanics.

Quantum mechanics and classical physics Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.[19] According to the correspondence principle between classical and quantum mechanics, all objects obey the laws of quantum mechanics, and classical mechanics is just an approximation for large systems of objects (or a statistical quantum mechanics of a large collection of particles). The laws of classical mechanics thus follow from the laws of quantum mechanics as a statistical average at the limit of large systems or large quantum numbers. However, chaotic systems do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems. Quantum coherence is an essential difference between classical and quantum theories, and is illustrated by the Einstein-Podolsky-Rosen paradox, Einstein's attempt to disprove quantum mechanics by an appeal to local realism.[20] Quantum interference involves adding together probability amplitudes, whereas classical "waves" infer that there is an adding together of intensities. For microscopic bodies, the extension of the system is much smaller than the coherence length, which gives rise to long-range entanglement and other nonlocal phenomena that are characteristic of quantum systems. Quantum coherence is not typically evident at macroscopic scales — although an exception to this rule can occur at extremely low temperatures (i.e. approaching absolute zero), when quantum behavior can manifest itself on more macroscopic scales.[21] This is in accordance with the following observations: • Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (which consists of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics. • While the seemingly "exotic" behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with particles of extremely small size or velocities approaching the speed of light, the laws of classical Newtonian physics remain accurate in predicting the behavior of the vast majority of "large" objects (on the order of the size of large molecules or bigger) at velocities much smaller than the velocity of light.[22] Quantum mechanics 89

Relativity and quantum mechanics Even with the defining postulates of both Einstein's theory of general relativity and quantum theory being indisputably supported by rigorous and repeated empirical evidence and while they do not directly contradict each other theoretically (at least with regard to their primary claims), they have proven extremely difficult to incorporate into one consistent, cohesive model.[23] Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly contributing to the field, he did not accept many of the more "philosophical consequences and interpretations" of quantum mechanics, such as the lack of deterministic causality. He is famously quoted as saying, in response to this aspect, "My God does not play with dice". He also had difficulty with the assertion that a single subatomic particle can occupy numerous areas of space at one time. However, he was also the first to notice some of the apparently exotic consequences of entanglement, and used them to formulate the Einstein-Podolsky-Rosen paradox in the hope of showing that quantum mechanics had unacceptable implications if taken as a complete description of physical reality. This was 1935, but in 1964 it was shown by John Bell (see Bell inequality) that - although Einstein was correct in identifying seemingly paradoxical implications of quantum mechanical nonlocality - these implications could be experimentally tested. Alain Aspect's initial experiments in 1982, and many subsequent experiments since, have definitively verified quantum entanglement. According to the paper of J. Bell and the Copenhagen interpretation—the common interpretation of quantum mechanics by physicists since 1927 - and contrary to Einstein's ideas, quantum mechanics was not, at the same time a "realistic" theory and a "local" theory. The Einstein-Podolsky-Rosen paradox shows in any case that there exist experiments by which one can measure the state of one particle and instantaneously change the state of its entangled partner - although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information happens. Quantum entanglement forms the basis of quantum cryptography, which is used in high-security commercial applications in banking and government. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of quantum gravity is an important issue in cosmology and the search by physicists for an elegant "Theory of Everything" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th and 21st century physics. Many prominent physicists, including Stephen Hawking, have labored for many years in the attempt to discover a theory underlying everything. This TOE would combine not only the different models of subatomic physics, but also derive the four fundamental forces of nature - the strong force, electromagnetism, the weak force, and gravity - from a single force or phenomenon. While Stephen Hawking was initially a believer in the Theory of Everything, after considering Gödel's Incompleteness Theorem, he has concluded that one is not obtainable, and has stated so publicly in his lecture "Gödel and the End of Physics" (2002).[24]

Attempts at a unified field theory The quest to unify the fundamental forces through quantum mechanics is still ongoing. Quantum electrodynamics (or "quantum electromagnetism"), which is currently (in the perturbative regime at least) the most accurately tested physical theory, Wikipedia:Identifying reliable sources(blog) has been successfully merged with the weak nuclear force into the electroweak force and work is currently being done to merge the electroweak and strong force into the electrostrong force. Current predictions state that at around 1014 GeV the three aforementioned forces are fused into a single unified field, Beyond this "grand unification," it is speculated that it may be possible to merge gravity with the other three gauge symmetries, expected to occur at roughly 1019 GeV. However — and while special relativity is parsimoniously incorporated into quantum electrodynamics — the expanded general relativity, currently the best theory describing the gravitation force, has not been fully incorporated into quantum theory. One of the leading authorities continuing the search for a coherent TOE is Edward Witten, a theoretical physicist who formulated the Quantum mechanics 90

groundbreaking M-theory, which is an attempt at describing the supersymmetrical based string theory. M-theory posits that our apparent 4-dimensional spacetime is, in reality, actually an 11-dimensional spacetime containing 10 spatial dimensions and 1 time dimension, although 7 of the spatial dimensions are - at lower energies - completely "compactified" (or infinitely curved) and not readily amenable to measurement or probing. Another popular theory is Loop quantum gravity (LQG), a theory that describes the quantum properties of gravity. It is also a theory of quantum space and quantum time, because in general relativity the geometry of spacetime is a manifestation of gravity. LQG is an attempt to merge and adapt standard quantum mechanics and standard general relativity. The main output of the theory is a physical picture of space where space is granular. The granularity is a direct consequence of the quantization. It has the same nature of the granularity of the photons in the quantum theory of electromagnetism or the discrete levels of the energy of the atoms. But here it is space itself which is discrete. More precisely, space can be viewed as an extremely fine fabric or network "woven" of finite loops. These networks of loops are called spin networks. The evolution of a spin network over time, is called a spin foam. The predicted size of this structure is the Planck length, which is approximately 1.616×10−35 m. According to theory, there is no meaning to length shorter than this (cf. Planck scale energy). Therefore LQG predicts that not just matter, but also space itself, has an atomic structure. Loop quantum Gravity was first proposed by Carlo Rovelli.

Philosophical implications Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. Even fundamental issues, such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated by society and many leading scientists. Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics."[25] The Copenhagen interpretation - due largely to the Danish theoretical physicist Niels Bohr - remains the quantum mechanical formalism that is currently most widely accepted amongst physicists, some 75 years after its enunciation. According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered a final renunciation of the classical idea of "causality". It is also believed therein that any well-defined application of the quantum mechanical formalism must always make reference to the experimental arrangement, due to the complementarity nature of evidence obtained under different experimental situations. Albert Einstein, himself one of the founders of quantum theory, disliked this loss of determinism in measurement. Einstein held that there should be a local hidden variable theory underlying quantum mechanics and, consequently, that the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the Einstein-Podolsky-Rosen paradox. John Bell showed that this "EPR" paradox led to experimentally testable differences between quantum mechanics and local realistic theories. Experiments have been performed confirming the accuracy of quantum mechanics, thereby demonstrating that the physical world cannot be described by any local realistic theory. The Bohr-Einstein debates provide a vibrant critique of the Copenhagen Interpretation from an epistemological point of view. The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes. This is not accomplished by introducing some "new axiom" to quantum mechanics, but on the contrary, by removing the axiom of the collapse of the wave packet. All of the possible consistent states of the measured system and the measuring apparatus (including the observer) are present in a real physical - not just formally mathematical, as in other interpretations - quantum superposition. Such a superposition of consistent state combinations of different systems is called an entangled state. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we can observe only the universe (i.e., the consistent state contribution to the aforementioned superposition) that we, as observers, inhabit. Everett's interpretation is perfectly consistent with John Bell's experiments and makes them intuitively understandable. However, according to the theory of quantum decoherence, Quantum mechanics 91

these "parallel universes" will never be accessible to us. The inaccessibility can be understood as follows: once a measurement is done, the measured system becomes entangled with both the physicist who measured it and a huge number of other particles, some of which are photons flying away at the speed of light towards the other end of the universe. In order to prove that the wave function did not collapse, one would have to bring all these particles back and measure them again, together with the system that was originally measured. Not only is this completely impractical, but even if one could theoretically do this, it would have to destroy any evidence that the original measurement took place (to include the physicist's memory!); in light of these Bell tests, Cramer (1986) formulated his transactional interpretation.[26] Relational quantum mechanics appeared in the late 1990s as the modern derivative of the Copenhagen Interpretation.

Applications Quantum mechanics had enormous[27] success in explaining many of the features of our world. Quantum mechanics is often the only tool available that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). Quantum mechanics has strongly influenced string theories, candidates for a Theory of Everything (see reductionism). Quantum mechanics is also critically important for understanding how individual atoms combine covalently to form molecules. The application of quantum mechanics to chemistry is known as quantum chemistry. Relativistic quantum mechanics can, in principle, mathematically describe most of chemistry. Quantum mechanics can also provide quantitative insight into ionic and covalent bonding processes by explicitly showing which molecules are energetically favorable to which others, and the magnitudes of the energies involved. Furthermore, most of the calculations performed in modern computational chemistry rely on quantum mechanics. A great deal of modern technological inventions operate at a scale where quantum effects are significant. Examples include the laser, the transistor (and thus the microchip), the electron microscope, and magnetic resonance imaging (MRI). The study of semiconductors led to the invention of the diode and the transistor, which are indispensable parts of modern electronics systems and devices.

Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to more fully develop quantum cryptography, which will A working mechanism of a resonant tunneling diode device, based on the phenomenon of theoretically allow guaranteed secure quantum tunneling through potential barriers transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum information over arbitrary distances.

Quantum tunneling is vital to the operation of many devices - even in the simple light switch, as otherwise the electrons in the electric current could not penetrate the potential barrier made up of a layer of oxide. Flash memory Quantum mechanics 92

chips found in USB drives use quantum tunneling to erase their memory cells. While quantum mechanics primarily applies to the atomic regimes of matter and energy, some systems exhibit quantum mechanical effects on a large scale - superfluidity, the frictionless flow of a liquid at temperatures near absolute zero, is one well-known example. Quantum theory also provides accurate descriptions for many previously unexplained phenomena, such as black body radiation and the stability of the orbitals of electrons in atoms. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures. Recent work on photosynthesis has provided evidence that quantum correlations play an essential role in this basic fundamental process of the plant kingdom. Even so, classical physics can often provide good approximations to results otherwise obtained by quantum physics, typically in circumstances with large numbers of particles or large quantum numbers.

Examples

Free particle For example, consider a free particle. In quantum mechanics, there is wave-particle duality, so the properties of the particle can be described as the properties of a wave. Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over space as a wave function. The position and momentum of the particle are observables. The Uncertainty Principle states that both the position and the momentum cannot simultaneously be measured with complete precision. However, one can measure the position (alone) of a moving free particle, creating an eigenstate of position with a wavefunction that is very large (a Dirac delta) at a particular position x, and zero everywhere else. If one performs a position measurement on such a wavefunction, the resultant x will be obtained with 100% probability (i.e., with full certainty, or complete precision). This is called an eigenstate of position—or, stated in mathematical terms, a generalized position eigenstate (eigendistribution). If the particle is in an eigenstate of position, then its momentum is completely unknown. On the other hand, if the particle is in an eigenstate of momentum, then its position is completely unknown.[28] In an eigenstate of momentum having a plane wave form, it can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the eigenstate.

3D confined electron wave functions for each eigenstate in a Quantum Dot. Here, rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular dots are more ‘s-type’ and ‘p-type’. However, in a triangular dot, the wave functions are mixed due to confinement symmetry. Quantum mechanics 93

Step potential

The potential in this case is given by:

The solutions are superpositions of left- and right-moving waves:

where the wave vectors are related to the energy via

, and Scattering at a finite potential step of height V , shown in green. The amplitudes and 0 direction of left- and right-moving waves are indicated. Yellow is the incident wave, blue are reflected and transmitted waves, red does not occur. E > V for this figure. and the coefficients A and B are 0 determined from the boundary conditions and by imposing a continuous derivative on the solution. Each term of the solution can be interpreted as an incident, reflected, or transmitted component of the wave, allowing the calculation of transmission and reflection coefficients. In contrast to classical mechanics, incident particles with energies higher than the size of the potential step are still partially reflected.

Rectangular potential barrier This is a model for the quantum tunneling effect, which has important applications to modern devices such as flash memory and the scanning tunneling microscope.

Particle in a box

The particle in a one-dimensional potential energy box is the most simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and infinite potential energy everywhere outside' that region. For the one-dimensional case in the direction, the time-independent Schrödinger equation can be written as:[29]

Writing the differential operator 1-dimensional potential energy box (or infinite potential well)

the previous equation can be seen to be evocative of the classic kinetic energy analogue

with as the energy for the state , which in this case coincides with the kinetic energy of the particle. The general solutions of the Schrödinger equation for the particle in a box are: Quantum mechanics 94

or, from Euler's formula,

The presence of the walls of the box determines the values of C, D, and k. At each wall (x = 0 and x = L), ψ = 0. Thus when x = 0,

and so D = 0. When x = L,

C cannot be zero, since this would conflict with the Born interpretation. Therefore, sin kL = 0, and so it must be that kL is an integer multiple of π. And additionally,

The quantization of energy levels follows from this constraint on k, since Quantum mechanics 95

Finite potential well This is the generalization of the infinite potential well problem to potential wells of finite depth.

Harmonic oscillator

As in the classical case, the potential for the quantum harmonic oscillator is given by:

This problem can be solved either by solving the Schrödinger equation directly, which is not trivial, or by using the more elegant "ladder method", first proposed by Paul Dirac. The eigenstates are given by:

Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wavefunction), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C,D,E,and F) are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.

where H are the Hermite polynomials: n

and the corresponding energy levels are

.

This is another example which illustrates the quantization of energy for bound states. Quantum mechanics 96

Notes [1] The angular momentum of an unbound electron, in contrast, is not quantized. [2] Max Born & Emil Wolf, Principles of Optics, 1999, Cambridge University Press

[3] http:/ / www. ias. ac. in/ resonance/ December2010/ p1056-1059. pdf [4] Reprinted in The collected papers of Albert Einstein, John Stachel, editor, Princeton University Press, 1989, Vol. 2, pp. 149-166, in German; see also Einstein's early work on the quantum hypothesis, ibid. pp. 134-148.

[5] http:/ / mooni. fccj. org/ ~ethall/ quantum/ quant. htm

[6] Compare the list of conferences presented here (http:/ / ysfine. com/ ) [7] P.A.M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford, 1930. [8] D. Hilbert Lectures on Quantum Theory, 1915-1927 [9] J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932 (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955). [10] H.Weyl "The Theory of Groups and Quantum Mechanics", 1931 (original title: "Gruppentheorie und Quantenmechanik").

[11] , Chapter 1, p. 52 (http:/ / books. google. com/ books?id=gCfvWx6vuzUC& pg=PA52)

[12] , Chapter 8, p. 215 (http:/ / books. google. com/ books?id=5t0tm0FB1CsC& pg=PA215)

[13] , Chapter , p. (http:/ / books. google. com/ books?id=W2J2IXgiZVgC& pg=PA265)

[14] Dict.cc (http:/ / www. dict. cc/ german-english/ eigen. html)

De.pons.eu (http:/ / de. pons. eu/ deutsch-englisch/ eigen)

[15] , Chapter 2, p. 36 (http:/ / books. google. com/ books?id=_qzs1DD3TcsC& pg=PA36)

[16] http:/ / th-www. if. uj. edu. pl/ acta/ vol19/ pdf/ v19p0683. pdf [17] Nancy Thorndike Greenspan, "The End of the Certain World: The Life and Science of Max Born" (Basic Books, 2005), pp. 124-8 and 285-6.

[18] http:/ / ocw. usu. edu/ physics/ classical-mechanics/ pdf_lectures/ 06. pdf [19] See, for example, Precision tests of QED. The relativistic refinement of quantum mechanics known as quantum electrodynamics (QED) has been shown to agree with experiment to within 1 part in 108 for some atomic properties.

[20] A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? (http:/ / www.

drchinese. com/ David/ EPR. pdf) Phys. Rev. 47 777 (1935). (http:/ / prola. aps. org/ abstract/ PR/ v47/ i10/ p777_1) [21] (see macroscopic quantum phenomena, Bose-Einstein condensate, and Quantum machine)

[22] http:/ / assets. cambridge. org/ 97805218/ 29526/ excerpt/ 9780521829526_excerpt. pdf [23] "There is as yet no logically consistent and complete relativistic quantum field theory.", p. 4. — V. B. Berestetskii, E. M. Lifshitz, L P Pitaevskii (1971). J. B. Sykes, J. S. Bell (translators). Relativistic Quantum Theory 4, part I. Course of Theoretical Physics (Landau and Lifshitz) ISBN 0-08-016025-5

[24] Stephen Hawking; Gödel and the end of physics (http:/ / www. damtp. cam. ac. uk/ strings02/ dirac/ hawking/ ) [25] The Character of Physical Law (1965) Ch. 6; also quoted in The New Quantum Universe (2003), by Tony Hey and Patrick Walters

[26] The Transactional Interpretation of Quantum Mechanics (http:/ / www. npl. washington. edu/ npl/ int_rep/ tiqm/ TI_toc. html) by John Cramer. Reviews of Modern Physics 58, 647-688, July (1986) [27] See, for example, the Feynman Lectures on Physics for some of the technological applications which use quantum mechanics, e.g., transistors (vol III, pp. 14-11 ff), integrated circuits, which are follow-on technology in solid-state physics (vol II, pp. 8-6), and lasers (vol III, pp. 9-13).

[28] , Chapter 6, p. 79 (http:/ / books. google. com/ books?id=XRyHCrGNstoC& pg=PA79)

[29] Derivation of particle in a box, chemistry.tidalswan.com (http:/ / chemistry. tidalswan. com/ index. php?title=Quantum_Mechanics)

References The following titles, all by working physicists, attempt to communicate quantum theory to lay people, using a minimum of technical apparatus. • Malin, Shimon (2012). Nature Loves to Hide: Quantum Physics and the Nature of Reality, a Western Perspective (Revised ed.). World Scientific. ISBN 978-981-4324-57-1. • Chester, Marvin (1987) Primer of Quantum Mechanics. John Wiley. ISBN 0-486-42878-8 • Richard Feynman, 1985. QED: The Strange Theory of Light and Matter, Princeton University Press. ISBN 0-691-08388-6. Four elementary lectures on quantum electrodynamics and quantum field theory, yet containing many insights for the expert. • Ghirardi, GianCarlo, 2004. Sneaking a Look at God's Cards, Gerald Malsbary, trans. Princeton Univ. Press. The most technical of the works cited here. Passages using algebra, trigonometry, and bra-ket notation can be passed over on a first reading. Quantum mechanics 97

• N. David Mermin, 1990, "Spooky actions at a distance: mysteries of the QT" in his Boojums all the way through. Cambridge University Press: 110-76. • Victor Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus Books. Chpts. 5-8. Includes cosmological and philosophical considerations. More technical: • Bryce DeWitt, R. Neill Graham, eds., 1973. The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press. ISBN 0-691-08131-X • Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. ISBN 0-19-852011-5. The beginning chapters make up a very clear and comprehensible introduction. • Hugh Everett, 1957, "Relative State Formulation of Quantum Mechanics," Reviews of Modern Physics 29: 454-62. • Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (1965). The Feynman Lectures on Physics 1–3. Addison-Wesley. ISBN 0-7382-0008-5. • Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-111892-7.

OCLC 40251748 (http:/ / www. worldcat. org/ oclc/ 40251748). A standard undergraduate text. • Max Jammer, 1966. The Conceptual Development of Quantum Mechanics. McGraw Hill. • Hagen Kleinert, 2004. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,

3rd ed. Singapore: World Scientific. Draft of 4th edition. (http:/ / www. physik. fu-berlin. de/ ~kleinert/ b5) • Gunther Ludwig, 1968. Wave Mechanics. London: Pergamon Press. ISBN 0-08-203204-1 • George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN 0-486-43517-2. • Albert Messiah, 1966. Quantum Mechanics (Vol. I), English translation from French by G. M. Temmer. North Holland, John Wiley & Sons. Cf. chpt. IV, section III. • Omnès, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8.

OCLC 39849482 (http:/ / www. worldcat. org/ oclc/ 39849482). • Scerri, Eric R., 2006. The Periodic Table: Its Story and Its Significance. Oxford University Press. Considers the extent to which chemistry and the periodic system have been reduced to quantum mechanics. ISBN 0-19-530573-6 • Transnational College of Lex (1996). What is Quantum Mechanics? A Physics Adventure. Language Research

Foundation, Boston. ISBN 0-9643504-1-6. OCLC 34661512 (http:/ / www. worldcat. org/ oclc/ 34661512). • von Neumann, John (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press. ISBN 0-691-02893-1. • Hermann Weyl, 1950. The Theory of Groups and Quantum Mechanics, Dover Publications. • D. Greenberger, K. Hentschel, F. Weinert, eds., 2009. Compendium of quantum physics, Concepts, experiments, history and philosophy, Springer-Verlag, Berlin, Heidelberg.

Further reading

• Bernstein, Jeremy (2009). Quantum Leaps (http:/ / books. google. com/ books?id=j0Me3brYOL0C& printsec=frontcover). Cambridge, Massachusetts: Belknap Press of Harvard University Press. ISBN 978-0-674-03541-6. • Müller-Kirsten, H. J. W. (2012). Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral (2nd ed.). World Scientific. ISBN 978-981-4397-74-2. • Bohm, David (1989). Quantum Theory. Dover Publications. ISBN 0-486-65969-0. • Eisberg, Robert; Resnick, Robert (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). Wiley. ISBN 0-471-87373-X. • Liboff, Richard L. (2002). Introductory Quantum Mechanics. Addison-Wesley. ISBN 0-8053-8714-5. Quantum mechanics 98

• Merzbacher, Eugen (1998). Quantum Mechanics. Wiley, John & Sons, Inc. ISBN 0-471-88702-1. • Sakurai, J. J. (1994). Modern Quantum Mechanics. Addison Wesley. ISBN 0-201-53929-2. • Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8. • Cox, Brian; Forshaw, Jeff (2011). The Quantum Universe: Everything That Can Happen Does Happen. Allen Lane. ISBN 1-84614-432-9.

External links

• 3D animations, applications and research for basic quantum effects (http:/ / www. toutestquantique. fr)

(animations also available in commons.wikimedia.org (https:/ / commons. wikimedia. org/ wiki/

Special:Contributions/ Jubobroff) (Université paris Sud)

• Quantum Cook Book (http:/ / oyc. yale. edu/ sites/ default/ files/ notes_quantum_cookbook. pdf) by R. Shankar, Open Yale PHYS 201 material (4pp)

• A foundation approach to quantum Theory that does not rely on wave-particle duality. (http:/ / www. mesacc.

edu/ ~kevinlg/ i256/ QM_basics. pdf)

• The Modern Revolution in Physics (http:/ / www. lightandmatter. com/ lm/ ) - an online textbook.

• J. O'Connor and E. F. Robertson: A history of quantum mechanics. (http:/ / www-history. mcs. st-andrews. ac. uk/

history/ HistTopics/ The_Quantum_age_begins. html)

• Introduction to Quantum Theory at Quantiki. (http:/ / www. quantiki. org/ wiki/ index. php/ Introduction_to_Quantum_Theory)

• Quantum Physics Made Relatively Simple (http:/ / bethe. cornell. edu/ ): three video lectures by Hans Bethe

• H is for h-bar. (http:/ / www. nonlocal. com/ hbar/ )

• Quantum Mechanics Books Collection (http:/ / www. freebookcentre. net/ Physics/ Quantum-Mechanics-Books. html): Collection of free books Course material

• Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics). (http:/ / arxiv. org/

abs/ quant-ph/ 0605180)

• MIT OpenCourseWare: Chemistry (http:/ / ocw. mit. edu/ OcwWeb/ Chemistry/ index. htm).

• MIT OpenCourseWare: Physics (http:/ / ocw. mit. edu/ OcwWeb/ Physics/ index. htm). See 8.04 (http:/ / ocw.

mit. edu/ OcwWeb/ Physics/ 8-04Spring-2006/ CourseHome/ index. htm)

• Stanford Continuing Education PHY 25: Quantum Mechanics (https:/ / www. youtube. com/ stanford#g/ c/

84C10A9CB1D13841) by Leonard Susskind, see course description (http:/ / continuingstudies. stanford. edu/

courses/ course. php?cid=20072_PHY 25) Fall 2007

• 5½ Examples in Quantum Mechanics (http:/ / www. physics. csbsju. edu/ QM/ )

• Imperial College Quantum Mechanics Course. (http:/ / www. imperial. ac. uk/ quantuminformation/ qi/ tutorials)

• Spark Notes - Quantum Physics. (http:/ / www. sparknotes. com/ testprep/ books/ sat2/ physics/

chapter19section3. rhtml)

• Quantum Physics Online : interactive introduction to quantum mechanics (RS applets). (http:/ / www.

quantum-physics. polytechnique. fr/ )

• Experiments to the foundations of quantum physics with single photons. (http:/ / www. didaktik. physik.

uni-erlangen. de/ quantumlab/ english/ index. html)

• AQME (http:/ / www. nanohub. org/ topics/ AQME) : Advancing Quantum Mechanics for Engineers — by T.Barzso, D.Vasileska and G.Klimeck online learning resource with simulation tools on nanohub

• Quantum Mechanics (http:/ / www. lsr. ph. ic. ac. uk/ ~plenio/ lecture. pdf) by Martin Plenio

• Quantum Mechanics (http:/ / farside. ph. utexas. edu/ teaching/ qm/ 389. pdf) by Richard Fitzpatrick

• Online course on Quantum Transport (http:/ / nanohub. org/ resources/ 2039) FAQs Quantum mechanics 99

• Many-worlds or relative-state interpretation. (http:/ / www. hedweb. com/ manworld. htm)

• Measurement in Quantum mechanics. (http:/ / www. mtnmath. com/ faq/ meas-qm. html) Media

• PHYS 201: Fundamentals of Physics II (http:/ / oyc. yale. edu/ physics/ phys-201#sessions) by Ramamurti Shankar, Open Yale Course

• Lectures on Quantum Mechanics (https:/ / www. youtube. com/ view_play_list?p=84C10A9CB1D13841) by Leonard Susskind

• Everything you wanted to know about the quantum world (http:/ / www. newscientist. com/ channel/

fundamentals/ quantum-world) — archive of articles from New Scientist.

• Quantum Physics Research (http:/ / www. sciencedaily. com/ news/ matter_energy/ quantum_physics/ ) from Science Daily

• Overbye, Dennis (December 27, 2005). "Quantum Trickery: Testing Einstein's Strangest Theory" (http:/ / www.

nytimes. com/ 2005/ 12/ 27/ science/ 27eins. html?scp=1& sq=quantum trickery& st=cse). The New York Times. Retrieved April 12, 2010.

• Audio: Astronomy Cast (http:/ / www. astronomycast. com/ physics/ ep-138-quantum-mechanics/ ) Quantum Mechanics — June 2009. Fraser Cain interviews Pamela L. Gay. Philosophy

• "Quantum Mechanics" (http:/ / plato. stanford. edu/ entries/ qm) entry by Jenann Ismael in the Stanford Encyclopedia of Philosophy

• "Measurement in Quantum Theory" (http:/ / plato. stanford. edu/ entries/ qt-measurement) entry by Henry Krips in the Stanford Encyclopedia of Philosophy Article Sources and Contributors 100 Article Sources and Contributors

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XeniaKon, Xezlec, Xihr, Yamaguchi先 生, Yath, Yeahyeahkickball, Yellowdesk, Yintan, Yokabozeez, Yowhatsupdude, Zakuragi, Zarniwoot, Zenbullets, Zero over zero, Zhinz, Zigger, ZiggyZig, Zolot, Zondor, Zooloo, Zslevi, Александър, 2236 anonymous edits Image Sources, Licenses and Contributors 105 Image Sources, Licenses and Contributors

Image:Helium atom QM.svg Source: http://en.wikipedia.org/w/index.php?title=File:Helium_atom_QM.svg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: User:Yzmo File:Daltons symbols.gif Source: http://en.wikipedia.org/w/index.php?title=File:Daltons_symbols.gif License: Public Domain Contributors: Hystrix, JamAKiska, Kurzon, Qvarie, Tanner Swett, 1 anonymous edits File:Mendeleev's 1869 periodic table.png Source: http://en.wikipedia.org/w/index.php?title=File:Mendeleev's_1869_periodic_table.png License: Public Domain Contributors: Original uploader was Sadi Carnot at en.wikipedia File:Atom diagram.png Source: http://en.wikipedia.org/w/index.php?title=File:Atom_diagram.png License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Original uploader was Fastfission at en.wikipedia File:Bohr Model.svg Source: http://en.wikipedia.org/w/index.php?title=File:Bohr_Model.svg License: Public Domain Contributors: Myself File:Mass Spectrometer Schematic.svg Source: http://en.wikipedia.org/w/index.php?title=File:Mass_Spectrometer_Schematic.svg License: Public Domain Contributors: Devon Fyson File:Binding energy curve - common isotopes.svg Source: http://en.wikipedia.org/w/index.php?title=File:Binding_energy_curve_-_common_isotopes.svg License: Public Domain Contributors: User:Fastfission File:Wpdms physics proton proton chain 1.svg Source: http://en.wikipedia.org/w/index.php?title=File:Wpdms_physics_proton_proton_chain_1.svg License: Public Domain Contributors: see below File:Potential energy well.svg Source: http://en.wikipedia.org/w/index.php?title=File:Potential_energy_well.svg License: Public Domain Contributors: User:Bdesham, User:Koantum File:S-p-Orbitals.svg Source: http://en.wikipedia.org/w/index.php?title=File:S-p-Orbitals.svg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Benjah-bmm27, Sven, Umherirrender, 1 anonymous edits File:Atomic orbitals and periodic table construction.ogv Source: http://en.wikipedia.org/w/index.php?title=File:Atomic_orbitals_and_periodic_table_construction.ogv License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Jubobroff File:Isotopes and half-life.svg Source: http://en.wikipedia.org/w/index.php?title=File:Isotopes_and_half-life.svg License: Public Domain Contributors: BenRG Image:Atomic orbital energy levels.svg Source: http://en.wikipedia.org/w/index.php?title=File:Atomic_orbital_energy_levels.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: Richard Parsons (raster), Adrignola (vector) File:Fraunhofer lines.svg Source: http://en.wikipedia.org/w/index.php?title=File:Fraunhofer_lines.svg License: Public Domain Contributors: Fraunhofer_lines.jpg: nl:Gebruiker:MaureenV Spectrum-sRGB.svg: Phrood Fraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. 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Image:Stimulatedemission.png Source: http://en.wikipedia.org/w/index.php?title=File:Stimulatedemission.png License: GNU Free Documentation License Contributors: User:(Automated conversion),User:DrBob Image:Visible EM modes.png Source: http://en.wikipedia.org/w/index.php?title=File:Visible_EM_modes.png License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Gerbrant, Kri, Maxhurtz, TimVickers, WillowW Image:vertex correction.svg Source: http://en.wikipedia.org/w/index.php?title=File:Vertex_correction.svg License: Public Domain Contributors: User:Harmaa File:CollageFisica.jpg Source: http://en.wikipedia.org/w/index.php?title=File:CollageFisica.jpg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Aushulz File:GodfreyKneller-IsaacNewton-1689.jpg Source: http://en.wikipedia.org/w/index.php?title=File:GodfreyKneller-IsaacNewton-1689.jpg License: Public Domain Contributors: Algorithme, Beyond My Ken, Bjankuloski06en, Ecummenic, Grenavitar, Infrogmation, Kelson, Kilom691, Leyo, Porao, Saperaud, Semnoz, Siebrand, Soerfm, Sparkit, Thomas Gun, Trijnstel, Vonvon, Wikiklaas, Wknight94, Wst, Zaphod, 8 anonymous edits File:Einstein1921 by F Schmutzer 2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Einstein1921_by_F_Schmutzer_2.jpg License: Public Domain Contributors: Diego pmc, Emijrp, Frank C. 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