QUANTUM MECHANICS

(Physics 215C)

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 spring quarter will include:

Klein Gordon Equation. Conserved Current. Negative Energy States and Anti-Particles. First Order Formulation. Plane Wave Solutions and Wavepackets. Klein Paradox. Potential Scattering. Bound State Spectrum in Coulomb Potential. Non-Relativistic Limit of the Klein-Gordon Equation.

Dirac Equation. Properties of the Dirac Matrices. Lorentz Invariance. Free Particle Solutions. Negative Energy States, Dirac Hole Theory and Antiparticles. Angular Momentum and Spin. Conserved Current. Coupling to an Electromagnetic Field. Non-Relativistic Limit. Darwin Term and Thomas Correction. Hydrogen Atom Spectrum in the Dirac Theory. Constants of the Motion and Degeneracies.

Quantized Radiation Field. Photon Creation and Destruction Operators. N-Particle States. Interaction Hamiltonian. Electro-Magnetic Field Commutators. Vacuum Fluctuations. Spontaneous Emission. Radiative Corrections. Bethe’s Nonrelativistic Calculation of the Lamb Shift. Mass Renormalization. Scattering of Light by Charged Particles.

Non-Relativistic Second Quantization. Boson and Fermion Creation and Annihilation Operators. Number Operator. Fock Space. Field Operators. General Second Quantized Operators. Free Fermion Pair Correlation Function. The Boson Case. Photon Correlations and the Hanbury-Brown and Twiss Experiment. Degenerate Electron Gas. Perturbation Theory. Particle-Hole Representation.

General Quantization of Continuous Fields. Lagrangian and Hamiltonian Densities. Fundamental Commutation Relations. Non-Relativistic Schrödinger Equation as a Field Equation. Equivalence to Second Quantization.

Recommended Books:

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

Intermediate Quantum Mechanics, by H. Bethe and R. Jackiw (Addison Wesley, 1985);

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

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

Advanced Quantum Mechanics, by J.J. Sakurai (Addison Wesley, 1967).

Herbert W. Hamber, PSII 3172 (x5596).

hhamber@uci.edu