Course abstract

This course has evolved out of the following courses offered for M.Sc. (Physics) students at IITMadras: Quantum Mechanics I (Core course) Quantum Mechanics II (Core course) Atomic and Molecular Physics (Core Course) Theory of Atomic Collisions and Spectroscopy (Elective Course). The curriculum will be covered in Ten Units. Each 'unit' will be covered in five to six lectures of 50 to 60 minutes each, as required by the course schedule. The course will begin with the identification of a complete set of compatible observables for the non-relativistic Hydrogen atom, identify the complete set of 'good quantum numbers', discuss the associated constants of motion and associated symmetries. The Laplace-Runge-Lenz vector and the Fock SO(4) symmetry of the Hydrogen atom will be discussed. The many-electron atom will be discussed in considerable detail, providing a thorough understanding of the Hartree-Fock Self-Consistent Field Formalism. This will be followed by the perturbative treatment of the spin-orbit interaction, effects of applied electromagnetic fields, hyperfine structure. An introduction to laser cooling of atoms and Bose-Einstein condensation will be provided. Subsequently, the semiclassical formalism of the theory of radiation based on first order time-dependent perturbation theory, Einstein's A and B coefficients, population inversion, and applications to lasers will be discussed. This will be followed by a detailed discussion on coupling of Angular Momenta, Clebsch-Gordan Coefficients, Statement and Proof the Wigner-Eckart Theorem and its applications in atomic spectroscopy. Spectroscopic terms and complex atomic spectra.In the second half of the course, Group Theoretical Methods will be used to demonstrate the applications of the Great Orthogonality Theorem. This will be followed by an introduction to electron-atom collisions, partial wave analysis, First and higher order Born approximation, the relativistic Hydrogen atom, Dirac equation. Foldy-Wouthuysen Transformation of Dirac Hamiltonian and Lamb shift. Symmetry and Conservation Laws in Atomic Physics will be introduced. Subsequently, molecular structure will be discussed along with 'nature of the chemical bond'. The course will conclude with an introduction to electronic, rotational, vibrational and ro-vibrational spectra of molecules, fragmentation dynamics of molecules, and an introduction to potential energy surface studies of the fragmentation dynamics.