- The Schrödinger equation: The Schrödinger equation; the uncertainty principle.
- One-dimensional systems: Free particle; particle in a box; the simple harmonic oscillator; potential wells; scattering and tunneling.
- Principles of quantum mechanics: States and operators; Hilbert space; probability and measurement; position and momentum representations.
- Three-dimensional systems: The Schrödinger equation in three dimensions; central potential; orbital angular momentum; the hydrogen atom.
- Angular momentum: Spin; general angular momentum; addition of angular momentum; Clebsch-Gordon coefficients.
- Many-particle systems: Identical particles; bosons and fermions.
- Perturbation theory: Time-independent perturbations; Zeeman effect; fine and hyperfine structures of the hydrogen atom; time-dependent perturbations*; two-level systems*.
- * Quantum information: EPR paradox; Bell inequality; quantum computation.