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.
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