Content: |
The course covers fundamental concepts: The Stern-Gerlach Experiment, Kets, Bras, and Operators, Base Kets and Matrix Representations, Measurements, Observables, and the Uncertainty Relations, Change of Basis, Position, Momentum, and Translation, Wave Functions in Position and Momentum Space, Quantum Dynamics: Time-Evolution and the Schrodinger Equation, The Schrodinger Versus the Heisenberg Picture, Simple Harmonic Oscillator, Schrodinger's Wave Equation, Elementary Solutions to Schrodinger's Wave Equation, Propagators and Feynman Path Integrals, Potentials and Gauge Transformations, Theory of Angular Momentum: Rotations and Angular-Momentum Commutation Relations, Spin 1/2 Systems and Finite Rotations, SO(3), SU(2), and Euler Rotations, Density Operators and Pure Versus Mixed Ensembles, Eigenvalues and Eigenstates of Angular Momentum, Orbital Angular Momentum, Schrodinger's Equation for Central Potentials, Addition of Angular Momenta Spin Correlation Measurements and Bell's Inequality, Tensor Operators, Approximation Methods: Time-Independent Perturbation Theory: Nondegenerate Case, Time-Independent Perturbation Theory: The Degenerate Case, Hydrogen-Like Atoms: Fine Structure and the Zeeman Effect. |