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, are prerequisites. Topics to be covered during the winter quarter will include:
· Orbital Angular Momentum. Commutation Relations. Differential Operator Representation. Rasing and Lowering Operators. Relation to the Laplacian. Legendre Polynomials. Spherical Harmonics. Eigenvalues and Eigenvectors of the Angular Momentum, using the Algebraic Method.
· Free Particle and the Three-Dimensional Square Well. Spherical Bessel Functions. The Two-Body Problem. Separation of the CMS Motion. Hydrogen Atom Spectrum. Laguerre Polynomials and Hydrogenic Wavefunctions. Angular and Radial Dependence of Orbitals. Degeneracies. Many-Electron Atoms.
· Particle in a Magnetic Field. Constant Magnetic Field, Exact Solution. Landau Levels. Normal Zeeman Effect. Bohm-Aharonov Effect.
· Spin One Half. Davisson and Germer Experiment. Pauli Matrices. Spin Magnetic Moment. Anomalous Zeeman Effect. Spin-Orbit Interaction. Thomas Precession. Addition of Two Angular Momenta. Stationary State Perturbation Theory.
· Identical Particles. Symmetric and Anti-Symmetric Wavefunctions. Bosons and Fermions. Exclusion Principle. Spin and Statistics Relation. Slater Determinants. Occupation Numbers. Free Fermi Gas and the Fermi Energy. Neutron Stars. Kronig-Penney Model, Band Structure in Solids. Two-Electron Atoms. Helium Spectrum. Raleigh-Ritz Variational Method. Exchange Integrals. Ferromagnetism. Positronium Spectrum.
Introduction to Quantum Mechanics, by R. Liboff (Addison Wesley, 1997);
Quantum Physics, by S. Gasiorowicz (Wiley, 1997).
Herbert W. Hamber, FRH 3172 (x5596).