ADVANCED QUANTUM MECHANICS 2

I. Advanced topics around the spin 1/2

1. Relativistic origin of the spin: Overview of the Lorentz group ; description as SU(2)xSU(2) ; representations ; introduction of the spinors

2. Dirac equation: Derivation ; weakly relativistic limit ; Pauli Hamiltonian

3. Applications: Low energy limit of the Dirac equation ; spin-orbit coupling ; fine structure of the hydrogen atom ; some words about the hyperfine structure of the hydrogen atom ; (very low energy) application: graphene

II. Second quantization

1. Introduction: Non conservation of particle number and the need for second quantization ; reminders about the free boson and fermions gases

2. Formal aspects : Fock spaces ; creation and annihilation operators ; the field operators ; some words about quantum field theory ; notion of quasiparticles

3. Low energy applications : A. Introduction to superconductivity:
Field theory ; mean field treatment ; Bogoliubov transformation ; zero temperature and finite temperature gap equation. B. Introduction the the Bose condensation phenomenon
Mean field theory ; bosonic Bogoliubov transformation ; life-time of Bogoliubov quasiparticles

The Advanced Quantum Mechanics 2 course is given by Edouard Boulat.

Edouard Boulat is professor at Université de Paris.