DOCSLIB.ORG

Syllabus & Lecture Notes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Syllabus & Lecture Notes 1 I. SYLLABUS AND INTRODUCTION Let us start with a brief overview of the items that will (hopefully) be covered in this course and to give a guideline of what we are trying to learn. Quantum mechanics 660 and 661 are advanced quantum mechanics courses designed for graduate students. The courses will be treated as a one-year course. It will be assumed that students have already some background in quantum mechanics (the concepts of waves, quantization, expectation values, etc.). An advised introductory text- book is Introduction to quantum mechanics by Griffiths. A number of things will, however, be repeated albeit in a more mathematical fashion. Also some basic knowledge in Fourier analysis, differential equations and linear algebra (calculation of eigenvalues and eigenstates) will be expected. All the information you need to know are in the lecture notes. However, the lecture notes are relatively concise and further reading is recommended. The book that was used last year was Liboff, Introductory Quantum Mechanics, fourth edition. However, a lot of other books treat the material of 660 in a similar fashion, so pick a book that you like best. Some of the material is not covered in Liboff (the older editions don’t have relativistic quantum mechanics and quite a bit of the material of 661 is not in there). The course is developed from a physicists point of view. Some concepts and mathematical techniques will be intro- duced along the way (such as matrix techniques) under the assumption that most of you are already somewhat familiar with them (after all, there are also 3 and 4 hundred level quantum mechanics courses). For a more comprehensive view of those things, I will refer to the textbook. The subjects that will be covered are History, Planck’s quantum hypothesis, photoelectric effect,specific heat, atomic physics. • The introduction is somewhat different from what is usually given in textbooks. However, since most of you have already followed a quantum mechanics course and since this is a graduate course, I think it is interesting to do it this way. Quite some time will be devoted to Planck’s hypothesis. The physical language is quite different from that of the rest of the course (it is more thermodynamics than quantum mechanics). Some of these things are treated in the exercizes of Chapter 2 of Liboff. Other things will be mentioned more briefly. Wave mechanics, Schr¨odinger equation, probability density, free particles, Heisenberg’s uncertainty principle. • This section tries to show some of the thinking that led to the Schr¨odinger equation. As soon as you leave the idea of a particle as a billiard ball behind you, a number of other things follow directly, such as Heisenberg’s uncertainty principle. Harmonic oscillator, Schr¨odinger equation approach, Solution using operators, Operators and wavefunctions, • Correspondence principle. Although most of you have seen the harmonic oscillator already, it is an important example, since the number of exactly solvable models in quantum mechanics is limited. Try to pay special attention to the two approaches to attack this problem. The Schr¨odinger approach, solving the differential equation for the wavefunction, and the algebraic or operator approach due to Heisenberg, Jordan, and Born. Although the Schr¨odinger approach is more intuitive, the operator approach will become more important as we go on, since often we do not really care that much about the wavefunction, but we are more interested in the spectral properties (energies) Of the problem. The Hydrogen atom, Legendre polynomials, angular momentum, matrix notation. • Again pay attention to the dual approach to this problem. The Schr¨odinger approach (solving the wavefunction) and the operator approach (angular momentum). This involves quite a bit of mathematics (solving differential equations). Here we will only deal with the potential from the nucleus, leading to the orbitals of the atom. Other aspects follow in the next section. Relativistic quantum mechanics, Klein-Gordan equation, Dirac equation, spin-orbit coupling. • This section introduces the Dirac equation and its consequences for the problems that we are interested in: the introduction of spin, relativistic correction to the Hydrogen atom (spin-orbit coupling, lowest order kinetic corrections). We could introduce (which would have been simpler) these aspects in a phenomenological or semi quantum/classical approach, but this is more fun and avoids having to treat relativistic quantum mechanics as some appendix. Note that we are not really interested in things such as time dilation, length contraction, etc. Perturbation theory and absorption and emission of photons, time-independent perturbation theory, • time-dependent perturbation theory, interaction of radiation and atom To be able to describe the emission and absortion of photons by an atom, we discuss perturbation theory. This will be done in some detail because of its relevance to later problems. Many-electron atom Pauli’s exclusion principle, the Helium atom, periodic table, Coulomb interactions, • addition of angular momenta. 2 FIG. 1: Left: The radiation spectrum of the sun at the top of the atmosphere (yellow) and at sea level (red) compared with a blackbody spectrum for 5250◦C. Right: Max Planck in 1901, around the time he developed the law now named after him. Source: wikipedia Having solved the atom for one electron, we would like to fill it with more electrons. First, we need to discuss a peculiar aspect of electrons (or fermions in general), namely the exclusion principle. We start with the simplest many-electron atom, Helium. We soon discover that electron-electron interaction have a strong influence and see that things are not as simple as suggested by the Hydrogen atom solution. We continue with a more general discussion of Coulomb interaction between electrons and how to couple the electron wavefunction in a smart way (LS-coupling). Molecules and solids, Hydrogen molecule, solids, (nearly) free-electron model. • We then continue by taking two atoms amd bringing them close together, thereby forming a molecule. If we continue adding atoms, we can form a one-dimensional solid, this is known as a tight-binding approximation. We can also approach it from the other side, by viewing a solid as a box of free electrons. The periodic potential has a only a small, but important, effect. Second quantization, the Coulomb gas. • We have a look at the ground-state energy of the electron gas and calculate it in the Hartree-Fock limit. We also see what the effect are of screening. II. OLD QUANTUM MECHANICS A. Planck’s quantum hypothesis The quantum theory started with the blackbody radiation. All matter emits electromagnetic radiation when its temperature is above abolute zero. The radiation results from the conversion of thermal energy into electromagnetic energy. A black body is a systems that absorbs all incident radiation. On the other hand, this also makes it the best possible emitter. It is hard to find a perfect black body, but, for example, graphite, is a good approximation. However, even when a system is not a perfect black body, the basic phenomena remains the same. The sun can, for example, be described to a good approximation as a black body, see Fig. 1. The spectral distribution has a maximum and decays for small and large wavelengths. For the sun which has an effective temperature of around 5500 K, the maximum lies in the visible region of the electromagnetic spectrum and is inherently related to the fact that the sun is white (and not yellow or even yellowish). Before Max Planck took up the subject there was already a surprising 3 Intensity Harb. un.L 0.25 0.20 0.15 0.10 0.05 E HeVL 0 1 2 3 4 5 FIG. 2: The blue line shows the Planck distribution as a function of energy for T = 5523 K. The brown line shows Wien’s distribution curve. The magenta line is the Rayleigh-Jeans law. amount of understanding of the spectral distribution predominantly due to Wilhelm Wien (1864-1928). For his work, he received the Nobel prize for Physics in 1911. Using general thermodynamic arguments, Wien showed in 1893 that the energy dependence is given by ω u(ω)= ω3f( ), (1) T where ω = 2πν and f is a function that only depends on the ratio ω/T , where T is the temperature. The function ω f( T ) cannot be derived from these considerations, but it can only be a function of ω/T or λT when expressed in the wavelength λ. The consequence of that is that the maximum occurs at a particular value of T/λ. Therefore, if the temperature changes the maximum occurs at a different wavelength. The human body can also be viewed as a far-from-perfect black body. The maximum occurs for a wavelength 9 λmax,SunTSun 525 10− 5500 λmax,human = = × = 9 µm, (2) Thuman 310 ∼ ω which is in the far infrared. Obviously, we would like to understand that the function f( T ) is. Wien made an ω educated guess that f( T ) = exp( aω/T ), where a is a constant. This dependence was obviously inspired by the Boltzmann factor and is a surprisingly− good guess, see Fig. 2. However, there is something strange about using the Boltzmann factor. The factor exp( E/kBT ), where kB is Boltzmann’s constant, implies that there is some finite energy associated with exciting electromagnetic− radiation. This is in complete contradiction with the classical way of thinking. The energy density of electro-magnetic radiation is given by 1 ε E2 + 1 B2, and therefore determined by 2 0 2µ0 the magnitudes of the electric and magnetic fields. Since we can take any possible value of these fields, any possible value of of the energy density is possible.
Load more

Recommended publications
  • Electron Diffraction V2.1
    Electron Diffraction v2.1 Background. This experiment demonstrates the wave-like nature of an electron as first postulated by Louis de Brogile in 1924. All particles including electrons have a wavelength inversely related to momentum: l = h/p. (1) It was well known at the time that the light could be diffracted by a periodic grating, where the grating period is of the order of the electromagnetic wavelength. If an electron has wave properties, then there might be a suitable physical grating to diffract it. Max von Laue had first suggested that periodic planes of atoms in a solid could serve as a grating. X- ray reflection experiments of Lawrence Bragg confirmed this and gave an estimate of the inter- Davisson and Germer in 1927 atomic spacing. Planes of atoms in a solid can also provide the appropriate grating spacing to cause electron diffraction. In a Nobel Prize winning experiment at Bell Labs in New Jersey, Clinton Davisson and Lester Germer used crystalline nickel to diffract electrons and prove their existence as waves. An independent experiment was done around the same time by George Thomson in Scotland. This was foundational work for the transmission electron microscope (TEM). The present experiment uses an ultra-thin polycrystalline graphite layer in place of nickel as the diffraction grating. Graphite forms as single planes of carbon atoms in a hexagonal arrangement shown in Figure 1. Vertical planes are not chemically bonded to adjacent planes. Instead they are more loosely held by the electrostatic van der Waals force but the atoms are remain aligned vertically.
    [Show full text]
  • 1 the Principle of Wave–Particle Duality: an Overview
    3 1 The Principle of Wave–Particle Duality: An Overview 1.1 Introduction In the year 1900, physics entered a period of deep crisis as a number of peculiar phenomena, for which no classical explanation was possible, began to appear one after the other, starting with the famous problem of blackbody radiation. By 1923, when the “dust had settled,” it became apparent that these peculiarities had a common explanation. They revealed a novel fundamental principle of nature that wascompletelyatoddswiththeframeworkofclassicalphysics:thecelebrated principle of wave–particle duality, which can be phrased as follows. The principle of wave–particle duality: All physical entities have a dual character; they are waves and particles at the same time. Everything we used to regard as being exclusively a wave has, at the same time, a corpuscular character, while everything we thought of as strictly a particle behaves also as a wave. The relations between these two classically irreconcilable points of view—particle versus wave—are , h, E = hf p = (1.1) or, equivalently, E h f = ,= . (1.2) h p In expressions (1.1) we start off with what we traditionally considered to be solely a wave—an electromagnetic (EM) wave, for example—and we associate its wave characteristics f and (frequency and wavelength) with the corpuscular charac- teristics E and p (energy and momentum) of the corresponding particle. Conversely, in expressions (1.2), we begin with what we once regarded as purely a particle—say, an electron—and we associate its corpuscular characteristics E and p with the wave characteristics f and of the corresponding wave.
    [Show full text]
  • INDUSTRIAL STRENGTH by MICHAEL RIORDAN
    THE INDUSTRIAL STRENGTH by MICHAEL RIORDAN ORE THAN A DECADE before J. J. Thomson discovered the elec- tron, Thomas Edison stumbled across a curious effect, patented Mit, and quickly forgot about it. Testing various carbon filaments for electric light bulbs in 1883, he noticed a tiny current trickling in a single di- rection across a partially evacuated tube into which he had inserted a metal plate. Two decades later, British entrepreneur John Ambrose Fleming applied this effect to invent the “oscillation valve,” or vacuum diode—a two-termi- nal device that converts alternating current into direct. In the early 1900s such rectifiers served as critical elements in radio receivers, converting radio waves into the direct current signals needed to drive earphones. In 1906 the American inventor Lee de Forest happened to insert another elec- trode into one of these valves. To his delight, he discovered he could influ- ence the current flowing through this contraption by changing the voltage on this third electrode. The first vacuum-tube amplifier, it served initially as an improved rectifier. De Forest promptly dubbed his triode the audion and ap- plied for a patent. Much of the rest of his life would be spent in forming a se- ries of shaky companies to exploit this invention—and in an endless series of legal disputes over the rights to its use. These pioneers of electronics understood only vaguely—if at all—that individual subatomic particles were streaming through their devices. For them, electricity was still the fluid (or fluids) that the classical electrodynamicists of the nineteenth century thought to be related to stresses and disturbances in the luminiferous æther.
    [Show full text]
  • Quantum Interference of Molecules--Probing the Wave Nature of Matter
    Anu Venugopalan is on the faculty of the School of Basic and Applied Sciences, GGS Indraprastha University, Delhi. Her primary research interests are in the areas of Foundations of Quantum mechanics, Quantum Optics and Quantum Information. Address for Correspondence: University School of Basic and Applied Sciences, GGS Indraprastha University Kashmere Gate, Delhi - 11 0 453 e-mail: [email protected] arXiv:1211.3493v1 [physics.pop-ph] 15 Nov 2012 1 Quantum Interference of Molecules - Probing the Wave Nature of Matter Anu Venugopalan November 16, 2012 Abstract The double slit interference experiment has been famously described by Richard Feynman as containing the ”only mystery of quantum mechanics”. The history of quantum mechanics is intimately linked with the discovery of the dual nature of matter and radiation. While the double slit experiment for light is easily undert- sood in terms of its wave nature, the very same experiment for particles like the electron is somewhat more difficult to comprehend. By the 1920s it was firmly established that electrons have a wave nature. However, for a very long time, most discussions pertaining to interference experiments for particles were merely gedanken experiments. It took almost six decades after the establishment of its wave nature to carry out a ’double slit interference’ experiment for electrons. This set the stage for interference experiments with larger particles. In the last decade there has been spectacular progress in matter-wave interefernce experiments. To- day, molecules with over a hundred atoms can be made to interfere. In the following we discuss some of these exciting developments which probe new regimes of Nature, bringing us closer to the heart of quantum mechanics and its hidden mysteries.
    [Show full text]
  • Interactions 2018
    Mellon College of Science | Carnegie Mellon University INTERACTIONS Department of Physics | 2018/2019 CONTENTS INTERACTIONS LETTER FROM DEPARTMENT HEAD, 02 Department of Physics SCOTT DODELSON Interactions is published yearly by the Department of Physics at Carnegie Mellon University for its students, alumni and friends to inform them FACULTY NOTES 03 about the department and serve as a channel of communication for our community. Readers with comments or questions are urged to send them to Interactions. Fax to 412-681-0648 or phone 412-268- 2740. The department is headed by Scott Dodelson. A QUANTUM AGE 14 Editor-in-Chief Scott Dodelson, Department Head Editor Jocelyn Duffy, Associate Dean for Communications Barry Luokkala, Teaching Professor Contributing Writers Joyce DeFrancesco, Jocelyn Duffy, Stephen Garoff, Barry Luokkala, Ben Panko, Emily Payne, Curtis Meyer, Lee Schumacher Graphic Design RESEARCH NOTES Rachel Wadell, Publications Manager 18 and Graphic Designer Photography and Images Courtesy of Carnegie Mellon University, unless otherwise noted Department of Physics Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 www.cmu.edu/mcs/physics STUDENT NOTES 21 Cover photo courtesy of: Gaia Data Processing and Analysis Consortium (DPAC); A. Moitinho / A. F. Silva / M. Barros / C. Barata, University of Lisbon, Portugal; H. Savietto, Fork Research, Portugal. Copyright: ESA/Gaia/DPAC, CC BY-SA 3.0 IGO PHYSICS STUDENTS 24 FIND INSPIRATION AT UNDERGRADUATE CONFERENCE FOR WOMEN Carnegie Mellon University does not discriminate in admission, employment, or administration of its programs or activities on the basis of race, color, national origin, sex, handicap or disability, age, sexual orientation, gender identity, religion, creed, ancestry, belief, veteran status, or genetic information.
    [Show full text]
  • An Explanation of the Double Slit Experiment Based on the Circles Theory
    Quantum Speculations 3 (2021) 33 - 52 Original Paper An Explanation of the Double Slit Experiment Based on the Circles Theory Mohammed Sanduk* Department of Chemical and Process Engineering, University of Surrey, Guildford, GU2 7XH, UK * Author to whom correspondence should be addressed; E-mail: [email protected] Received: 27 December 2020 / Accepted: 25 March 2021 / Published online: 31 March 2021 Abstract: The circles theory tries to explain the complex functioning of the harmonic oscillator. It is a non-quantum mechanics theory, but it shows a good similarity with the forms of equations of the relativistic quantum mechanics. The Circles Theory explains the association of the wave and the point that corresponds with the wave and particle of quantum mechanics. According to the circular motions of an individual system, a fluid model for a huge number of the circular system is expected to be formed. Then, a wave of fluid may appear. So, a real wave of fluid-type is seen due to the circular motion in addition to the wave associated with the point or the particle. In this article, the double slit experiment has been explained in accordance with the circles theory. According to the circles theory, the double slit experiment shows that this fluid-like wave is responsible for the interference pattern, whereas the associate wave is responsible for the uncertain location of the particle on the screen. On the other hand, the observation of the fluid may destroy the formulation of the wave of fluid. If this happens, then the interference disappears, but a pattern of shout bullets appears.
    [Show full text]
  • Deciphering the Enigma of Wave-Particle Duality Mani Bhaumik1 Department of Physics and Astronomy, University of California, Los Angeles, USA 90095
    Deciphering the Enigma of Wave-Particle Duality Mani Bhaumik1 Department of Physics and Astronomy, University of California, Los Angeles, USA 90095 A reasonable explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than a certainty, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be adequately understood. The reality of comprehending the wave function as an amplitude distribution of irregular disturbances imposes the necessity of acquiring the wave function in its entirety for detection. This is evinced by the observed certainty of wave function collapse that supports the paradigm of reality of the wave function portrayed in this article. 1. Introduction Ever since the advent of the wildly successful quantum theory nearly a century ago, its antecedent, wherein the wave aspect is always associated with a particle has been a source of great mystery to professional scientists and to the public as well.
    [Show full text]
  • Lecture 35 (De Broglie & Matter Waves)
    Lecture 35 (de Broglie & Matter Waves) Physics 2310-01 Spring 2020 Douglas Fields Symmetry • I’ve talked about symmetry in physics a lot… – The symmetry of the Maxwell’s equations in E and B (in vacuum, at least). – The symmetry of space and time in special relativity. – Many others • But the initial development of Quantum Mechanics is a beautiful example of how one can use symmetry to theorize something that has yet to be observed. • This was done by Louise-Victor de Broglie in his PhD thesis of 1924… Particle Waves • De Broglie hypothesized that since light waves behave like particles, perhaps particles should also behave like waves. • Since, for light: • Then, the same should also hold true for matter (or particles). • Hence, for a particle: • Which, of course, reduces in the limit of low v to: Particle Waves • Similarly, the frequency of a photon is given by its energy: • So, for a particle: • And, again, at low v, this reduces to: Overall phase factor that cancels in all physics measurements Particle Waves • So, from analogy with light, de Broglie postulated that: • So, let’s see if this gives us the correct velocity of the particle… Periodic Wave Description • Remember: y x Wave travelling to the right Periodic Wave Description • How fast is the wave moving? y x Wave Velocity • Let’s look at this in relation to what we (should) know about wave motion. • Since we know that the velocity of a wave is given by the angular frequency ω and wave number k, let’s calculate these: • And we take our normal way of finding the velocity of a wave: • Crap.
    [Show full text]
  • I Don't Understand Quantum Physics
    I Don't Understand Quantum Physics by Douglas Ross FRS Emeritus Professor of Physics, University of Southampton i Contents 1 Introduction - Understanding \understanding". 1 2 Some Classical Physics 3 2.1 Waves .......................................3 2.1.1 Interference and Diffraction . .4 2.1.2 Wavepackets . .5 2.1.3 Travelling and Standing Waves . 14 2.2 Particles . 15 3 Experiments that Shook the World of Physics. 22 3.1 The Ultraviolet Catastrophe . 22 3.2 The Photoelectric Effect. 25 3.3 Compton Scattering . 27 3.4 Bragg X-ray Diffraction . 29 3.5 The Davisson-Germer Experiment . 30 4 Wave-Particle Duality 34 4.1 Both a wave and a particle . 34 4.2 Which Slit did the particle go through? . 35 5 What is a Matter (de Broglie) Wave? 37 6 Particles and Fields 39 7 Heisenberg's Uncertainty Principle 41 8 Wavefunctions - Schr¨odinger'sEquation 44 8.1 Discrete Energy Levels . 44 8.1.1 Particle in a Box (in one dimension) . 44 8.1.2 Harmonic Oscillator . 46 8.1.3 The Hydrogen Atom . 47 ii 9 Quantum Tunnelling 51 10 Quantum States and Superposition 53 11 Two State Systems 55 11.1 Photon Polarization . 55 11.2 Electron Spin . 57 12 Wavefunction Collapse 61 12.1 Decoherence . 62 13 Interpretations of Quantum Physics 64 13.1 Copenhagen Interpretation . 64 13.2 Many Worlds Interpretation. 64 14 Two Enigmatic \Thought Experiments" 66 14.1 Schr¨odinger'sCat . 66 14.2 Einstein Rosen Podosky (EPR) Paradox - entanglement . 68 15 Hidden Variables 71 16 Why is the Quantum World so Small? 76 17 Probabilistic Determinism 78 18 Is Quantum Theory Correct and Complete? 80 iii Acknowledgments I am extremely grateful to Laurence Baron, Alexander Belyaev, Jean-Michel Jakobow- icz, David Pugmire, Joe Stroud and Anthony Warshaw for reading earlier versions of this manuscript and making a number of helpful suggestions for improving the clarity of the text.
    [Show full text]
  • Crystallographic Career of Sidney Cyril Abrahams
    Sidney Cyril Abrahams was a crystallographer at Bell Labs for 31 years, a charter member of the ACA and its president in 1968. As part of the ACA History Project, he describes here his career as a crystallographer, also as editor of Acta Crystallographica. Sidney’s full narrative will be deposited at the Center for the History of Physics (AIP). This article is part of an ongoing series by individual crystallographers. If you would like to contribute your story, contact Virginia Pett, [email protected]. Born May 28, 1924 in London, England and educated at Ilford County High School 1935-1938 and Greenock Academy 1938-1942, the present writer graduated BSc with first class honors in chemistry from the University of Glasgow in 1946, where J. Monteath Robertson was Gardiner Professor of Chemistry. Entering graduate school under the supervision of JM, a pioneer of X-ray crystallography, was a “no brainer”. Working at the Royal Institution with such major figures as W. H. Bragg, W. T. Astbury, J. D. Bernal and K. Lonsdale, JM had become a founder of organic crystallography, an area in which he played a major role by his development of heavy-atom and isomorphous-replacement methods for solving the phase problem. JM’s research group in 1946 included Jack D. Dunitz, A. (Sandy) McL. Mathieson and John G. White, each of whom subsequently made valuable contributions to structural crystallography. In 1948, the summer before completing his PhD thesis, the writer received an invitation to participate in Massachusetts Institute of Technology’s coming summer term as one of 62 graduate students from 18 different European countries, four of whom were from the United Kingdom.
    [Show full text]
  • Davisson – Germer Experiment Announcements: • Homework Set 5 Is Today
    Davisson – Germer experiment Announcements: • Homework set 5 is today. • Homework set 6 will be posted later today. • Made a good guess about the Nobel Prize for 2013 Clinton Davisson and Lester Germer. Davisson won Nobel Prize in 1937. Germer didn’t! – No dynamite money! Today we will go over the Davisson-Germer experiment. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1 Lester Germer • Born on October 10, 1896, graduated from Cornell University in 1917. After graduation he joined Bell Labs and then served in World War I as a fighter pilot, earning a citation from General Pershing. After the war he returned to Bell Labs and finished his Ph.D. at Columbia University in 1927. • At Bell Labs, Germer initially worked as an assistant to Clinton Davisson. In April of 1925 Davisson and Germer began working on an experiment studying the diffraction of electrons off of a nickel surface. At first their results were similar to results obtained four years earlier. Then suddenly the results changed. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 2 Germer cont. • They performed a similar experiment in 1927, after Davisson had attended a conference where DeBroglie's hypothesis about the wave nature of matter was presented. When electrons of known velocity were used to bombard the nickel surface at a 45 degree angle they observed that the diffraction of the electrons obeyed Bragg's Law. This was the first proof of DeBroglie's particle wave hypothesis. • After this experiment Germer continued working at Bell Labs, studying the use of this technique to determine the structure of surfaces, work that eventually led to the development of the electron microscope.
    [Show full text]
  • Atomic and Nuclear Physics Physics
    LD Atomic and Nuclear Physics Physics Introductory experiments Leaflets P6.1.5.1 Dualism of wave and particle Diffraction of electrons in a polycrystalline lattice (Debye-Scherrer diffraction) Objects of the experiment g Determination of wavelength of the electrons g Verification of the de Broglie’s equation g Determination of lattice plane spacings of graphite Principles Louis de Broglie suggested in 1924 that particles could have wave properties in addition to their familiar particle properties. He hypothesized that the wavelength of the particle is in- versely proportional to its momentum: h λ = (I) p λ: wavelength h: Planck’s constant D1 p: momentum His conjecture was confirmed by the experiments of Clinton Davisson and Lester Germer on the diffraction of electrons at crystalline Nickel structures in 1927. In the present experiment the wave character of electrons is demonstrated by their diffraction at a polycrystalline graphite lattice (Debye-Scherrer diffraction). In contrast to the experi- ment of Davisson and Germer where electron diffraction is observed in reflection this setup uses a transmission diffrac- tion type similar to the one used by G.P. Thomson in 1928. From the electrons emitted by the hot cathode a small beam is singled out through a pin diagram. After passing through a focusing electron-optical system the electrons are incident as sharply limited monochromatic beam on a polycrystalline D graphite foil. The atoms of the graphite can be regarded as a 2 space lattice which acts as a diffracting grating for the elec- trons. On the fluorescent screen appears a diffraction pattern of two concentric rings which are centred around the indif- fracted electron beam (Fig.
    [Show full text]