Topics for Quantum Theory

Relevant paragraphs in Sakurai's book (S) are indicated for each topic. The material covered in the lectures and exercise classes determines the content of the course. The text book is for additional background and context.

  1. Fundamental concepts (S: 1.2-1.7, 2.1-2.2)
    position and momentum representation, states and operators (bra-ket notation), unitary transformations, Heisenberg equation of motion, Ehrenfest theorem, Hellmann-Feynman theorem, uncertainty relation
  2. Symmetry (S: 4.1,4.2,4.4)
    conservation laws, unitary and anti-unitary symmetries, parity, time-reversal, Kramers degeneracy, Galilean invariance
  3. Fermions and bosons (S: 2.3, 7.2, 7.5)
    creation/annihilation operators, fermionic/bosonic Fock space, field operators, coherent states, Bogoliubov and Majorana quasiparticles in a superconductor
  4. Quantum electrodynamics: (S: 2.7, 5.6, 7.6)
    gauge transformations, Byers-Yang theorem, Aharonov-Bohm effect, persistent current, Casimir effect
  5. Approximation methods (S: 2.5, 5.4)
    variational principle, semiclassics, Bohr-Sommerfeld quantization, WKB approximation, applications to resonant tunneling and Landau level quantization
  6. Time-dependent quantum systems (S: 5.6)
    adiabatic theorem, Landau-Zener transitions, Berry phase, applications to Dirac fermions in graphene
  7. Path integrals (S: 2.4, 2.6)
    Lagrangian, principle of least action, quantum propagator, Feynman path integral, stationary phase approximation