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