Calendar

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

Quantum Measurement, EPR, Bell Inequalities, Greenberger-Horne-Zeilinger