Other links:
Other links:
This course explores how the principles of quantum mechanics explain phenomena ranging from scattering and the formation of energy bands in solids to graphene and other forms of collective quantum matter. Along the way, students will encounter topics such as relativistic quantum mechanics, second quantization, the renormalization group, etc., ideas that lie at the heart of modern physics, from condensed matter to emerging quantum technologies.
Topics to be covered:
1. Relativistic QM: Dirac equation and Graphene
a. Dirac equation: Free particle problem, emergence of spin, negative energy problem
b. Graphene as a Dirac problem, Klein paradox and its resolution
d. Fermions: Weyl, Majorana, Dirac (Basic ideas)
2. Scattering
a. Scattering in one and three dimensions
A unified description of scattering, bound states, and resonances; Renormalization group
b. Lippmann-Schwinger equation; Born approximation; Rutherford scattering.
3. Introduction to many-body physics
a. Second quantization
b. Mean field approximations like Thomas-Fermi, Hartree, Hartree-Fock
c. Superconductivity: Cooper pairs, BCS wave-function, Landau-Ginzburg theory
Prerequisites: QM1, QM2
References
David Tong’s Lectures (Cambridge U website),
Mathews-Venkatesan/Shankar (for some of the topics).
somendra.bhattacharjee@ashoka.edu.in