Special Topics in Atomic Physics

Overview

Quantum Mechanics and the Symmetry of the hydrogen atom - Complete set of observables for the non-relativistic Hydrogen atom - radial and angular wavefunctions; Complete set of 'good quantum numbers - associated constants of motion and associated symmetries. The Laplace-Runge-Lenz vector and the Fock SO(4) symmetry of the Hydrogen atom - Coupling of Angular Momenta, Clebsch-Gordan Coefficients, Statement and Proof the Wigner-Eckart - Relativistic Hydrogen Atom. Foldy-Wouthuysen Transformation of Dirac Hamiltonian - Identical Particles; Exchange interaction and N-electron systems. The Hartree-Fock Self-Consistent Field Formalism. Koopmans Theorem - Perturbative analysis of relativistic interactions in atoms - Probing the atom quantum collisions and photoabsorption processes - Photoionization cross-section and angular distribution of the photoelectrons - Effects of applied electromagnetic fields. Stark effect. Zeeman effect (normal and anomalous) in atomic spectroscopy, Paschen-Back effect. Hyperfine structure. Introduction to laser cooling of atoms and Bose-Einstein condensation.