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%.

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