QUANTUM MECHANICS

(Physics 215A)

The course is intended as a graduate level presentation of the methods of Quantum Mechanics. It will be assumed that the student is already familiar with undergraduate level Quantum Mechanics. Undergraduate students will require consent of the instructor. Topics to be covered during the fall quarter will include:

Historical Retrospective. Black Body Radiation. Bohr’s Atom and the Old Quantum Theory. De Broglie Waves. Photon Polarizations, State Vectors and Amplitude Mechanics. Dirac Notation.

Schrödinger Wave Equation. Fermi Derivation. Stationary Solutions and other Special Cases. State Vectors and Operators. Hilbert Space. Hermitean and Unitary Operators. Free Particle. Motion of Wavepackets. Fundamental Commutator. Quantum Mechanical Motion as Sum over Paths. Feynman Path Integral for Free Particle. Aharonov Bohm Effect.

One-Dimensional Barrier Problems. Tunneling. Bound States. Parity. Analytic Properties of Transmission Amplitudes. Delta Function and Periodic Potentials. Harmonic Oscillator. Creation and Destruction Operators. Matrix Mechanics.

Formal Developments. Heisenberg Equations of Motion. Schrödinger and Heisenberg Picture. Unitary Time Evolution Operator. Time Ordering Operator.

Orbital Angular Momentum. Commutation Relations and Differential Operator Representation. Rotations. Spherical Harmonics. Central Forces. Hydrogen Atom. Dynamical Symmetries.

Stationary State Perturbation Theory. Degenerate Case. Applications (Van Der Waals Interactions, Electrons in a One-dimensional Lattice). Rayleigh-Ritz Variational Principle. WKB Semiclassical Approximation. Applications (Harmonic Oscillator).

Recommended Books:

Lectures on Quantum Mechanics, by G. Baym (Addison Wesley, 1973);

Quantum Mechanics, by E. Merzbacher (John Wiley, 1998);

Modern Quantum Mechanics, by J.J. Sakurai (Addison Wesley, 1985);

Quantum Mechanics, by L. Schiff (McGraw Hill, 1968);

Quantum Mechanics, by L. Landau and E. Lifshitz (Pergamon, 1967).

Herbert W. Hamber, PSII 3172 (x5596).

hhamber@uci.edu