| TOPICS | SUBTOPICS |
|---|---|
| Fundamental Concepts |
Introduction - Classical vs. Quantum Mechanics, Simple 2-state QM Example Mathematical Preliminaries - Hilbert Spaces, Operators The Rules of Quantum Mechanics - 4 Basic Postulates, More Spin 1/2 Observables - Compatible Observables, Tensor Product Spaces, Uncertainty Relations Position, Momentum and Translation - Dirac vs. Van Neumann Eigenvalue Problems - Operator, Shooting, Variational, Quantum Monte Carlo Methods |
| Time Evolution (Quantum Dynamics) |
Time Evolution and the Schrodinger Equation Schrodinger, Heisenberg and Interaction Pictures; Energy-time Uncertainty, Interpretation of Wavefunction Connections between Classical and Quantum Mechanics - Ehrenfest, Quantization, Path Integrals Quantum Particles in Potential and EM Fields - Gauge Invariance, Aharanov-Bohm, Magnetic Monopoles |
| Angular Momentum |
SO(3) vs. SU(2) Lie Algebra and Representations of SU(2) Spherical Harmonics Addition of Angular Momenta Tensor Operators and Wigner-Eckardt |
| Perturbation Theory |
Rayleigh-Schrodinger (Nondegenerate Time-independent) Perturbation Theory Structure of Equations Convergence of Series, Pade Approximants Degenerate Perturbation Theory Examples in Hydrogen Atom |
| Density Operators, Quantum Statistics and Measurement | Density Operators and Quantum Statistical Mechanics |
