The course is intended as an introduction to the methods of Quantum Mechanics. It will be assumed that the student has already some familiarity with ordinary and partial differential equations, linear algebra and Fourier transforms. Third-year courses in Electromagnetism and Classical Mechanics, as well as 113A & B, are prerequisites. Topics to be covered during the spring quarter will include:
· Hartree-Fock Approximation for Atoms. Correlation Energies. Hydrogen Molecule. Born-Oppenheimer Approximation.
· Time-Dependent Perturbation Theory. Interaction Representation. Fermi Golden Rule for Transition Rates. Case of Harmonic Perturbations.
· Interaction of Radiation with Matter. Semiclassical Theory. Light Absorption and Emission Rates. Einsteinís A and B Coefficients. Electric Dipole Transitions. Selection Rules. Qualitative Discussion of Magnetic Dipole and Electric Quadrupole Transitions.
· Collision Theory. Scattering Amplitude and Cross Section. Born Approximation. Phase Space Factors. Rutherford Cross-Section. Partial Wave Expansion and Phase Shifts. Scattering for Hard Spheres and Square Wells.
· Relativistic Wave Equations. Klein Gordon Equation. Dirac Equation. Properties of Dirac Matrices. Free Particle Solutions. Negative Energy States, Dirac Hole Theory and Antiparticles. Angular Momentum and Spin. Coupling to an Electromagnetic Field. Non-Relativistic Limit. Qualitative Discussion of the Hydrogen Atom Spectrum in the Dirac Theory.
Introduction to Quantum Mechanics, by R. Liboff (Addison Wesley, 1997);
Quantum Physics, by S. Gasiorowicz (Wiley, 1997).
Herbert W. Hamber, FRH 3172 (x5596).