PSI 2018/2019 - Condensed Matter (Tiwari)

Motivation; single-particle Schroedinger Eqn; N particles; symmetrizaion/anti-symmetrization; second quantization; Fock space.

Hamiltonian in second quantization.

Electrons in a periodic potential; Bravais lattice; Bloch's theorem; FIrst Brillouin Zone; Intro to nearly free electrons and tight binding model.

Tight binding model; Nearly free electrons (unperterbed solution, zone folding, brief discussion of unperturbed solution).

Peierl's theorem; Fermi surface; relative importance of average KE vs. average PE; density of states; Mean Field Theory.

Hartree and Hartree-Fock equations; Self-energy; Screening (Yukawa potential); Stoner model for ferromagnetism (Hubbard model).

Stoner model for ferromagnetism (Hubbard model); magnetic polarization; accoustic and optical phonons.

Quantum theory of phonons; Debye Model; electron-phoning interactions.

BSC theory

BSC theory; Kubo formula

BSC theory; Quantum Hall Effect