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.
- 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
- 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
- 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
- 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
- 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
- Time-dependent quantum systems (KP: 12.3 — B: 12.7)
adiabatic theorem, Landau-Zener transitions, Berry phase, applications to Dirac fermions in graphene
- 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