Advanced Quantum Physics Syllabus

Review of Quantum Physics: Postulates of quantum mechanics, operator methods, time-dependence, symmetry. Solutions to the Schrödinger equation in one dimension. Angular momentum and spin; matrix representations.

Motion of charged particle in electromagnetic fields: normal Zeeman effect; diamagnetic hydrogen; gauge invariance; Aharonov-Bohm effect; 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.

Identical particles: Particle indistinguishability and quantum statistics; free particle systems; effects of interactions.

Atomic and molecular structure: Revision of Hydrogen Atom. Fine structure: relativistic corrections; Spin-orbit coupling; hyperfine structure. Multi-electron atoms: LS coupling; Hund's rules; Zeeman effect. Born-Oppenheimer approximation; H2+ ion; molecular orbitals; H2 molecule; ionic and covalent bonding.

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

Elements of quantum field theory: Quantization of the classical atomic chain; phonons; rules of field quantization and quantum electrodynamics; number states, coherent states, non-classical light.

Advanced Quantum Physics

Syllabus

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