Quantum Mechanics III
### Quantum Mechanics III (Spring '10)

This course will mainly deal with nonrelativistic many particle quantum
systems. I will not use any single book as such, but a blend of various
material.

Books (text+reference): Feynman, Lectures on Statistical Mechanics (mainly);
R. Mattuck, A guide to Feynman diagrams in the many-body problem, G.
Mahan, Many particle systems; A. Altland, B. Simons, Condensed matter
field theory; Sakurai, Advanced quantum mechanics; also a seemingly nice
book is P. Phillips, Advanced solid state physics;

Course outline (broadly): second quantised formulation of many particle
systems, quantization of nonrelativistic free fields, phonons, quantum
systems of many identical particles, fermion systems, ground state and
particle-hole operators, electron-phonon systems, polarons, electron
hopping models, spin systems (in particular the Ising model and the
Jordan-Wigner transformation to free fermions and discussion thereof from
Sachdev's Quantum phase transitions), Coulomb-interaction-induced
corrections to the electron gas ground state energy and Feynman diagrams,
superconductivity [some basic phenomenological properties, London equation
and the Landau-Ginzburg macroscopic description, microscopic BCS theory
(zero temp, no current), Bogoliubov de Gennes equations and transport
between normal metals and superconductors (single electron incidence,
specular reflection, Andreev reflection)].
Final lectures will discuss scaling towards the Fermi surface,
Wilsonian ideas of renormalization and the relevance of the BCS
interaction (as in Polchinski's "Eff. field theory and the Fermi
surface", arxiv:hep-th/92xxxxx).

Regular (weekly) assignments (incorporated into class): 15%

Midsem exam, 35%,

Endsem exam, 50%.

back to home