PSI 2017/2018 - Condensed Matter (Tiwari)

First quantization for many-particle systems, Slater determinants and permanents

Fock space, creation and annihilation operators, one- and two-particle operators in second quantization

Bravais lattices, reciprocal lattices, electrons in a periodic potential, Bloch's theorem

First Brillouin zone, tight-binding model, nearly-free electrons

Perturbation theory for nearly-free electrons, Peierl's theorem, electron-electron interactions, jellium model

Jellium model, Hartree and Fock terms, density of states, jellium oscillations and Einstein phonons

Classical description of phonons, quantum theory of phonons, Debye model

Electron-phonon interactions, Schrieffer-Wolff transformation

Mean field theory, Hartree-Fock approximation, screening, Stoner model for ferromagnetism

Stoner model for ferromagnetism, goals of the BCS theory of superconductivity, the Cooper problem

The Cooper problem, BCS theory

BCS ground state, BCS excitations from mean-field theory