| Course Outline: |
14 weeks, lectures
(3 times a week), recitation (once a week)
Introduction
Old Quantum Theory, Bohr model, De Broglie, duality
Interference and Diffraction-Young's experiments for light, single slit
diffraction, two slit interference of electrons, superposition principle,
probability amplitude
Uncertainty Principle-Life time of atomic scale, 3 level and 4 level lasers,
stimulated emission, coherence, superposition
Wave Packets-Uncertainty principle, Fourier integral
Schroedinger Equation-Deduction of equation from traveling wave for free
particles, expectation value operators, introduction to free electron
model
Infinite Potential Well-Deduction of wave functions from free particle
wave, expectation values, uncertainty
Stationary State Theory-Time independent equation, eigenvalues, eigenfunctions
Transition State Theory-Hydrogen atom transitions, time dependent probabilities
Well Behaved Eigenfunctions for Finite Potential Step--Curvature of wave
function, general solution of time independent Shroedinger equation for
classically allowed and forbidden states
Finite Steps-Reflection probability, tunneling, finite barrier E>Vo
and E<Vo tunneling
Applications of Tunneling-STM, a-decay, nuclear fission, fission reactor,
tunnel diode, ammonia inversion, maser
Finite Well-Infinite wall, 1D, 3D, separation of variables, harmonic oscillator,
ionic bonding, bond-energy diagram
Coulomb Potential-Multi-electron atom, Hartree, many atom solid
Pauli Principle-Antisymmetric eigenfunctions, covalent bonding in H2,
F2, N2, O2, sp3 hydrids, Hund's rule
Molecular Orbitals
Spectroscopies, Selection Rules
Free Electron Theory-Drude classical theory, electrical and thermal conductivity,
specific heat
Sommerfeld Free Electron-Cyclic boundary conditions, traveling wave in
periodic lattice, k space representation of solutions of Schroedinger
equation
Fermi Sphere, Energy, Radius-Calculations for Ag, density of states, average
energy of electron in free electron gas, bulk modulus, compare with classical
picture
Experimental Confirmation of Free Electron Picture-Soft x-rays, UV photoemission,
measurement of band width, density of state, work function, Na, Mg, Al,
concept of sp bands
Fermi-Dirac Statistics-Boltzmann approximation, specific heat of electrons,
electrical and thermal conductivity in metals
Energy Width of Isolated Conduction Band-sp bands, shape of density of
allowed states, monovalent, divalent, trivalent metals, density of occupied
states, d bands in Cu and Ni
Effective Mass-Band mass, interactions with lattice
Nearly Free Electron theory-Bragg condition at top of band, traveling
waves, standing waves, include crystal potential, remove degeneracy, band
gap, Kronig-Penney band overlap
Evolution of Conduction Band-Valence band, conduction band, s, sp, sp3
bands, change of magnitude of band gap, insulator to metal transition
Introduction to Semiconductors-Maxwell-Boltzmann approximation to Fermi-Dirac,
calculation of electron, hole concentration in Ge, position of Fermi level,
comparison of carrier concentration and conductivity in Ge and Si
Quantum Confinement-Comparison of semiconductors and metals, excitons,
plasmon, optical properties
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