Session 1: Solid State Physics Classical vs. Quantum Mechanics 1 1. Intro 2. Birth of QM Outline 3. Schrod. Eq 4. Simple Prob. Introduction History Thomson’s atomic model Rutherford’s atomic model Birth of QM Black body radiation Photoelectric effect Bohr model Uncertainty principle Double slit Schrodinger Equation Probability density Operators Postulates of QM Simple problems free electron / particle in box / potential wall / tunneling / Kronig-Penning problem / Harmonic oscillator 2 1. Intro 2. Birth of QM History of Chemistry 3. Schrod. Eq 4. Simple Prob. In fourth century B.C., ancient Greeks proposed that matter consisted of fundamental particles called atoms. Over the next two millennia, major advances in chemistry were achieved by alchemists. Their major goal was to convert certain elements into others by a process called transmutation. In 400 B.C. the Greeks tried to understand matter (chemicals) and broke them down into earth, wind, fire, and air. air hot fire wet dry water cold earth Relation of the four ELEMENTS and the four qualities 3 1. Intro 2. Birth of QM History of Chemistry 3. Schrod. Eq 4. Simple Prob. Serious experimental efforts to identify the elements began in the eighteenth century with the work of Lavoisier , Priestley , and other chemists. By the end of the nineteenth century , about 80 of the elements had been correctly identified, John Dalton (1766–1844) The law of definite proportions was correctly interpreted by the Teacher of James Joule English chemist John Dalton as evidence for the existence of atoms. Dalton argued that if we assume that carbon and oxygen are composed of atoms whose masses are in the ratio 3:4 and if CO is the result of an exact pairing of these atoms (one atom of C paired with each atom of O), ELEMENTS DISCOVERED BEFORE 1800: (Italicized if discovered after 1700) H -- -- -- -- C N O -- -- -- -- -- -- P S Cl -- -- -- -- Ti -- Cr Mn Fe Co Ni Cu Zn -- -- As -- -- -- -- -- -- -- -- Mo -- -- -- -- Ag -- -- Sn Sb Te -- -- -- -- -- -- -- W -- -- -- Pt Au Hg -- Pb Bi -- -- -- -- -- -- -- -- U 4 1. Intro 2. Birth of QM Thomson’s Atomic Model 3. Schrod. Eq 4. Simple Prob. Proposed about 1900 by Lord Kelvin and strongly supported by Sir Joseph John Thomson, ⊝ ƍ Thomson’s “plum-pudding” model of the atom had the ƍ ⊝ positive charges spread uniformly throughout a sphere the ƍ ⊝ ⊝ ƍ size of the atom, with electrons embedded in the uniform ⊝ ƍ ⊝ ƍ ⊝ background. ƍ ⊝ ƍ ƍ ⊝ J. J. Thomson (1856 – 1940) Nobel Prize: 1906 Teacher of Ernest Rutherford and 6 other Nobel winners Father of G. P. Thomson (Nobel 1937) “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” --- Lord Kelvin, 1900 5 1. Intro 2. Birth of QM Rutherford’s Atomic Model 3. Schrod. Eq 4. Simple Prob. Rutherford Scattering (1909): The experimental results were not consistent with Thomson’s atomic model. Ernest Rutherford(1871 –1937) New Zealand-born father of nuclear physics Nobel Prize in Chemistry (1908) Rutherford proposed (1911) that an atom has a positively charged core (nucleus) surrounded by the negative electrons 6 1. Intro 2. Birth of QM Failing of the Planetary Model 3. Schrod. Eq 4. Simple Prob. From classical E&M theory, an accelerated electric charge radiates energy (electromagnetic radiation) which means total energy must decrease. Radius r must decrease!! Electron crashes into the nucleus!? Nucleus Physics had reached a turning point in 1900 with Planck’s hypothesis of the quantum behavior of radiation. 7 1. Intro 2. Birth of QM Am I Classical or Quantum? 3. Schrod. Eq 4. Simple Prob. An Electron! classical quantum mass, energy, momentum photoelectric effect, diffraction Wave-Particle Duality deBroglie wavelength = Planck’s constant = 6.63×10 -34 J·s (measured) Ɣ ͜⁄ ͤ ͜ = momentum ͤ = wavelength Is electron like a soccer ball or not? Who knows! 8 1. Intro 2. Birth of QM Wave-Particle Duality 3. Schrod. Eq 4. Simple Prob. How do I look? vs. = 100Kg = 1Kg 1Kg = 1 m/s ͡ ͡ ͡= ≅ 1 m/s ͪ ͪ = 6.6×10 -34 m Ɣ? = 6.6×10 -4 m -31 = 0.5 J = 5×10 J 32 ̿ = E/h = 7.5×10 /s ̿ = 757/s ͚ ͚ 9 1. Intro 2. Birth of QM Black Body Radiation 3. Schrod. Eq 4. Simple Prob. • Temperature is just average energy in each microscopic degree of motion ( (1/2)kT, k = Boltzman’s constant) • Every object radiates light at its intrinsic frequencies of vibration etc. • A Black Body absorbs all light incident, but must re-radiate light, whose intensity and spectrum depends only upon the temperature. Classical Mechanics, and Classical EM gave prediction for black body radiation that: 1. Disagreed with experiments 2. Was logically inconsistent (Infinite total energy). Planck (1900 ) found that a very simple formula could be Max Planck (1858 – 1947) used to calculate the quantum at a particular frequency of Nobel Prize (1918) EMR E = energy of the radiation (J) ̿ Ɣ ͚͜ h = Planck’s Constant = 6.63e-34 J·s f = frequency of the EMR (Hz) 10 1. Intro 2. Birth of QM Photo Electric Effect 3. Schrod. Eq 4. Simple Prob. • Light shining on a metal will liberate electrons, but the photon energy hf must be greater than a threshold energy (equal to binding energy of electron in metal.) • The threshold effect is independent of light intensity (energy density of light). • Na requires 2.5eV = Green In 1905 an unknown physicist named Albert Einstein came up with an idea that built on what Planck had said. The light consist of particles named photon . Photon comes from the Greek word for light. Einstein originally called photons a “light quantum.” The chemist Gilbert N. Lewis came up with the name photo. 11 1. Intro 2. Birth of QM Fathers of QM! 3. Schrod. Eq 4. Simple Prob. Louis de Broglie (1892 –1987) Introduced wave-particle duality in his PhD thesis,Erwin 1924Schrödinger (1887 –1961) Nobel Prize in Physics, 1929 the Schrödinger equation, January 1926 Nobel MaxPrize Born in Physics, (1882 1933–1970) @ University of Göttingen, he came into contact with: Klein, Hilbert, Minkowski, Werner Heisenberg (1901 –1976) Runge, Schwarzschild, and Voigt Physical interpretation of the Sch ‘s wave function Student of Summerfeld/Born Matrix mechanics Matrix mechanicsPascual / JordanUncertainty (1902 Principle – 1980) Nobel Prize in Physics, 1954 Nobel Prize in Physics, 1932 Paul Dirac ( 1902 –1984) Student of Born Matrix mechanics Fermi–Dirac statistics special theory of relativity + quantum mechanics ‘quantum field theory’ Nobel Prize in Physics, 1933 12 1. Intro 2. Birth of QM H2 Emission & Absorption Spectra 3. Schrod. Eq 4. Simple Prob. Sun and stars are made of Hydrogen and Helium, The galaxies are receding from us (redshift) Balmer Series [Joseph Balmer, 1885] 1 1 Ɣ ͌ ͦ Ǝ ͦ ,͢ Ɣ 3,4,5,… 2 ͢ 13 1. Intro 2. Birth of QM Photon Emission 3. Schrod. Eq 4. Simple Prob. With -19 If = Δ̿ 440 Ɣnm, ͗͜/λ = 4.5 x 10 J λ Δ̿ Energy Emission “Continuous” spectrum “Quantized” spectrum are allowed are Δ̿ Δ̿ Δ̿ Energy Energy ispossible Δ̿ Any Any Only certain Onlycertain 14 1. Intro 2. Birth of QM Bohr Atomic Model 3. Schrod. Eq 4. Simple Prob. Introduced by Niels Bohr (1885 –1962) in 1913, a Dane, proposed his model of the atom while working at Cambridge University in England Atom: a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus (similar to the solar system) 15 1. Intro 2. Birth of QM Bohr Atomic Model 3. Schrod. Eq 4. Simple Prob. Louis de Broglie wave-particle duality his 1924 thesis(1892 –1987) Ɣ ͜⁄ ͤ 11 years later ! ͪͦ͡ Ɣ ͢ň de Broglie standing wave ̿! ͜ Ɣ ̿$ Ǝ ̿! Bohr’s postulate̿$ (1913): (1) An electron in an atom moves in a circular orbit about the nucleus under the influence of the Coulomb attraction between the electron and the nucleus, obeying the laws of classical mechanics. (2) An electron move in an orbit for which its orbital angular momentum is , Planck’s constant ͆(3) Ɣ An ͢ň electron Ɣ ͢͜⁄ 2with , ͢ constant Ɣ 1,2, ⋯ acceleration͜ moving in an allowed orbit does not radiate electromagnetic energy. Thus, its total energy remains constant. (4) Electromagnetic radiation is emitted if an electron,̿ initially moving in an orbit of total energy , discontinuously changes its motion so that it moves in an orbit of total energy ̿$ . The frequency of the emitted radiation is . ̿! Ɣ ʚ̿$ Ǝ ̿!ʛ⁄͜ 16 1. Intro 2. Birth of QM Bohr’s Model 3. Schrod. Eq 4. Simple Prob. ͦ ͦ ͦ ͦ 1 ͔͙ ͪ ͙ ̀ Ɣ ͕͡ → ͦ Ɣ ͡ ͢ ň ͤ ʱ → ͦ)Ɣ 4#ͤ ͦ 4# ͦ ͦ ͔͙͡ ͆ Ɣ ͪͦ͡ Ɣ ͢ň ͦ ̿ ͢ň 1 ͔͙ ͪ) Ɣ Ɣ ͦ͡) 4#ͤ ͢ň ͔͙ ͯϦ Potential energy: ͦ ͦ ͔͙ ͔͙ ͐ Ɣ Ǝ ǹ ͦ ͦ͘ ƔƎ ͤ ͤ - 4# ͦ 4# ͦ Kinetic energy: ͦ ͥ ͦ ͔͙ ͅ Ɣ ͦͪ͡ Ɣ 4#ͤʚ2ͦʛ Total energy: ̿ Ɣ ͅ ƍ ͐ Ɣ Ǝͅ ⟹ ͦ ͨ ͔͡ ͙ 1 ͦ 13.6 eV ̿) ƔƎ ͦ ͦ ͦ Ɣ Ǝ͔ ͦ 4 #ͤ 2ň ͢ ͢ 17 1. Intro 2. Birth of QM Bohr Atomic Model 3. Schrod. Eq 4. Simple Prob. wave-particle duality Ɣ ͜⁄ ͤ ͪͦ͡ Ɣ ͢ň de Broglie standing wave Energy Bands: ̿ͨ ̿ͧ ̿ͦ ͥ ̿ 18 1. Intro 2. Birth of QM Bohr’s Model 3. Schrod. Eq 4. Simple Prob.