**PHY ****603: Advanced Quantum Mechanics**** (4)**

*Learning Objectives*:

The course will be a review of foundations of quantum mechanics along with some advanced topics like approximation methods in quantum mechanics, atomic and molecular theory, time-dependent perturbation theory and scattering theory.

*Course Contents*:

Review of Quantum Mechanics Postulates of quantum mechanics, operator methods, matrix representations, time-dependence, symmetry : Unitary operators: translations in space, translation in time (evolution). Rotations, reflections and parity. Conservation laws.

Solutions to the Schrodinger equation in one dimension. Angular momentum and spin.

Charged particles in electromagnetic fields Hamiltonian for a charged spinless particle in an electromagnetic field. Gauge transformations and gauge nvariance. Aharonov-Bohm effect; Free electron in a uniform magnetic field: Landau levels.

*Approximate Methods:* Time-independent perturbation theory, first and second order expansion; Degenerate perturbation theory; Stark effect; nearly free electron model. Variational method: ground state energy and eigenfunctions; excited states. The WKB method: bound states and barrier penetration.

*Atomic and molecular structure:* Revision of the Hydrogen atom. Fine structure: relativistic corrections; spin-orbit coupling; hyperfine structure. Zeeman effects; diamagnetic hydrogen. Multi-electron atoms: central field approximation; LS coupling; Hund's rules. Born-Oppenheimer approximation; H_2+ ion; molecular orbitals; H_2 molecule; ionic and covalent bonding.

*Time-dependent perturbation theory:* Two-level system, Rabi oscillations, Magnetic resonance. Perturbation series, Fermi's Golden rule, scattering and Born approximation. Radiative transitions, dipole approximation, stimulated emission and absorption, spontaneous emission, Einstein's A and B coefficients, selection rules; Cavity rate equations and lasers.

*Scattering by a Potential:* Formalism; Born approximations; Partial wave analysis Relativistic Quantum Mechanics Klein-Gordan and Dirac equations and their solutions. Chirality and helicity.

*Suggested Books*:

- Quantum Physics, S. Gasiorowicz
- Quantum Mechanics: Non-Relativistic Theory, Volume 3, L. D. Landau and L. M. Lifshitz
- The Physics of Atoms and Quanta, H. Haken and H. C. Wolf Quantum Mechanics, F. Schwabl
- Principles of Quantum Mechanics, R. Shankar
- Problems in Quantum Mechanics, G. L. Squires
- Quantum Mechanics: A New Introduction, K. Konishi and G. Paffuti
- Quantum Mechanics, F. SchwablQuantum Mechanics, C. Cohen-Tannoudji, B.D. Franck Laloe

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