MSE 221 Quantum Physics of Materials
Elementary quantum concepts, wave mechanics, energy states, bonding, transitions,
electronic properties
Prerequisite: PHYS 151
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, -decay, nuclear fission, fission reactor, tunnel diode, ammonia
inversion, maser
Finite Well—Infinite wall, 1D, 3D, separation of variables, harmonic oscillator, ionic bonding, bondenergy 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