Topics for Quantum Theory

The book by Konishi and Paffuti is indicated by KP, while B refers to Ballantine's book. The material covered in the lectures and exercise classes determines the content of the course. The text books are for additional background and context.

  1. Basics (KP: 7 — B: 1-2, 3.7, 8.4)
    position and momentum representation, states and operators (bra-ket notation), unitary transformations, Heisenberg equations of motion, uncertainty relation, pure states and mixtures, density matrix
  2. Symmetry (KP: 5.0-5.2.4 — B: 3.1-3.3, 3.8, 13)
    conservation laws, unitary and anti-unitary symmetries, parity, time-reversal, Kramers degeneracy, Galilean invariance
  3. Fermions and bosons (KP: 3.4.2, 5.3, 20.10-20.11 — B: 17, 19.4)
    creation/annihilation operators, fermionic/bosonic Fock space, field operators, coherent states, Bogoliubov and Majorana quasiparticles in a superconductor
  4. Time-independent quantum systems (KP: 3.1-3.2, 10.1-10.2, 14.1-14.2 — B: 10.6, 11.1-11.2, 11.4)
    theorems (virial, oscillation, variational, Ehrenfest, Hellmann-Feynman, Byers-Yang), Aharonov-Bohm effect, persistent current
  5. Semiclassics (KP: 11.1.0, 11.2.0-11.2.1, 11.3.0, 14.3 — B: 11.3, 14.4)
    Bohr-Sommerfeld quantization, WKB approximation, resonant tunneling, Landau levels
  6. Time-dependent quantum systems (KP: 12.3 — B: 12.7)
    adiabatic theorem, Landau-Zener transitions, Berry phase, applications to Dirac fermions in graphene
  7. Path integrals (KP: 8.1-8.2.1, 20.1.1 — B: 4.8)
    Lagrangian, principle of least action, quantum propagator, Feynman path integral, stationary phase approximation