Part A Quantum Theory.
This course builds directly on the first course in quantum mechanics and covers a series of important topics, particularly features of systems containing several particles. The behaviour of identical particles in quantum theory is more subtle than in classical mechanics, and an understanding of these features allows one to understand the periodic table of elements and the rigidity of matter.
There are rarely neat solutions to problems involving several particles, so usually one needs some approximation methods. These are developed so as to study both energy levels of interacting Hamiltonians, and scattering.
Prof. Christopher Beem
Students will be able to demonstrate knowledge and understanding of the mathematics of quantum mechanics of many particle systems, and atomic structure and scattering.
Scattering and tunnelling in 1 dimension. Symmetries in quantum mechanics. Rotations, spin and angular momentum and their addition.
Identical particles, symmetric and anti-symmetric states, Fermi-Dirac and Bose-Einstein statistics and atomic structure.
Approximation methods, Rayleigh-Schrödinger time-independent perturbation theory and variation principles. The virial theorem. Helium. WKB approimation.
Heisenberg representation, interaction representation, time dependent perturbation theory and FeynmanDyson expansion, Fermi's golden rule.