Spring 2021: Applications of Quantum Mechanics - II (PHYS 6574)
Prerequisites: An introductory graduate level quantum mechanics course (at the same level as PHYS 6572 at Cornell). Undergraduate students are welcome to register for the course, after discussing with the instructor.
Overview: This is an advanced graduate level course that will discuss an assortment of advanced topics in quantum mechanics. The aim of this course is to enable students to develop a conceptual understanding of various fundamental aspects of quantum mechanics and a variety of technical skills.
Click here for additional course information, including tentative list of topics. The course is currently only available to Cornell affiliates. Course material is available on canvas.
Lectures:
L1 (02/09): Schrödinger vs. Heisenberg picture. Introduction to Interaction representation and time-ordering.
L2 (02/11): Introduction to time-dependent perturbation theory.
L3 (02/16): Linear response theory. Effect of a time-dependent electric field on induced polarization.
L4 (02/18): Dynamic polarizability and Semiclassical theory of optical absorption.
L5 (02/23): Semiclassical theory of optical absorption (contd.) and stimulated emission.
L6 (02/25): Photoelectric effect
L7 (03/02): Angle resolved photoemission spectroscopy
L8 (03/04): Born approximation from time-dependent perturbation theory. Fermi's golden rule.
L9 (03/11): Inelastic scattering from an atom with internal degrees of freedom.
L10 (03/16): Review of classical electromagnetism.
L11 (03/18): Quantization of electromagnetic field. Photon Hilbert space.
L12 (03/23): Field operators, vacuum fluctuations and normal ordering.
L13 (03/25): Quantization of electromagnetic field (contd.)
L14 (03/30): Charged particles in electromagnetic field.
L15 (04/01): Revisiting spontaneous radiation/photon absorption/stimulated emission.
L16 (04/06): Introduction to many-particle quantum mechanics. Indistinguishability and permutation operators.
L17 (04/08): Many-body Hilbert space and second quantization.
L18 (04/13): Single and two-particle operators in terms of field operators.
L19 (04/15): Ground state for non-interacting bosons vs. fermions. Wick's theorem.
L20 (04/20): Hartree-Fock approximation.
L21 (04/27): Hubbard model and antiferromagnetic exchange at strong interaction.
L22 (04/29): Quantum (anti)ferromagnetism in the semiclassical limit---Holstein-Primakoff transformations. Spontaneous symmetry breaking and Goldstone modes.
L23 (05/04): Mermin-Wagner-Hohenberg theorem. Quantum antiferromagnets without long-range order
L24 (05/06): Weakly interacting bosons and superfluidity.
L25 (05/11): Landau quasiparticles and Fermi liquids.
L26 (05/13): Cooper instability in a Fermi liquid.