| 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 |
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