QUANTUM MECHANICS

(Physics 215B)

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:

Time-Dependent Perturbation Theory. Interaction Representation. Dyson Series. Fermi Golden Rule. for Transition Rates. Harmonic Perturbations. Second Order Transitions. Total Rate and State Lifetime. Applications.

Interaction of Radiation with Matter. Hamiltonian. Currents and Gauge Invariance. Zeeman Effect. Semiclassical Theory. Light Absorption and Emission Rates. Einstein’s A and B Coefficients. Electric Dipole Transitions. Selection Rules. Sum Rule. Magnetic Dipole and Electric Quadrupole Transitions. Multipole Transitions. Scattering of Light by Matter. Thomson Cross Section.

Pauli Theory of Spin. Spin Matrix Algebra. Rotations in Spin Space. Spin Magnetic Moment. Zeeman Effect Revisited. Spin-Orbit Coupling, Relativistic Effects and Thomas Precession. Spin Precession.

Addition of Angular Momenta. Clebsch-Gordan Series. Addition of Three Angular Momenta. Racah Coeffficients. Isotopic Spin. Irreducible Representations of the Rotation Group. d Matrices and Spherical Harmonics. Tensor Operators. Wigner-Eckart Theorem. Product of Tensor Operators. Applications.

Identical Particles. Permutation Group. Symmetric and Anti-Symmetric States. Exclusion Principle. Slater Determinants. Two Electron Atoms. Hartree-Fock Approximation. Hydrogen Molecule. Born-Oppenheimer Approximation..

Potential Scattering. Integral Equation. Scattering Amplitude and Cross Section. Born Approximation. Partial Wave Expansion and Phase Shifts. Analytic Properties of the Scattering Amplitude. Width of a Resonance. Coulomb Scattering.

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