Advanced Quantum Mechanics of Many-Body Systems

fizyka

Knowledge of classical mechanics, quantum mechanics, electrodynamics, basis of statistical physics and thermodynamics, complex variable calculus, differential and integral calculus, matrix calculus, Fourier transforms.

w sali

The goal of this course is to introduce students to the mathematical formalism of non-relativistic quantum mechanics of many-body systems as well as give an overview of applications in condensed-matter physics.

1. Quantum mechanics of many-body systems; fermions and bosons.

2. Second quantization; field operators.

3. Green's and correlation functions and their applications.

4. Spontaneous symmetry breaking, mean-field theory.

5. Perturbation theory, Feynman diagrams.

6. Linear response theory.

7. Electromagnetic field quantization.

A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems

H. Bruus, K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics

A. Altland, B. Simons Condensed Matter Field Theory

J.W. Negele, H. Orland, Quantum many-paricle systems

R.D. Mattuck, A guide to Feynman diagrams in the many-body problems

S.M. Barnett, Quantum information

Knowledge:

- knowledge of second quantization formalism

- knowledge of Green's functions and correlation functions

Skills:

- solving stndard problems of nonrelativistic quantum mechanics of many-body systems

- description of physical phenomena in terms of simple mathematical models and correlation functions

- solving problems using field operators

- written test

- written exam

- oral exam