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Prerequisites

The Part II Advanced Quantum Physics course assumes knowledge of the Part IB NST Physics A and Physics B courses, especially the Quantum Physics course, and, to a lesser extent, the Dynamics and Electromagnetism courses.

Learning Outcomes and Assessment

The use of approximate methods in the analysis of quantum systems will be introduced, especially variational approaches and perturbation theory. These methods will be used to understand important features of atomic and molecular structure, to estimate the influence of external electric or magnetic fields on atomic energy levels, and to compute atomic transition rates and scattering cross sections. The importance of symmetries, especially rotational symmetry and identical particle symmetry, in quantum systems will be emphasised. Quantum field theory will be briefly introduced, in the context of photons in a quantised electromagnetic field.

Synopsis

Review of Quantum Physics: Postulates of quantum mechanics, operator methods, time-dependence. Solutions to the Schrödinger equation in one and three dimensions. Angular momentum and spin; matrix representations. Addition of angular momenta, Clebsch-Gordan coefficients.

Approximate Methods: Time-independent perturbation theory, first and second order expansion; Degenerate perturbation theory. Variational method: ground state energy and eigenfunctions.

Motion of charged particle in electromagnetic field: gauge invariance; Aharonov-Bohm effect. Particle magnetic moments; Stern-Gerlach experiment. Landau levels; the Quantum Hall Effect.

Symmetries: Translations and rotations, parity. Conservation laws. The Wigner-Eckart theorem for scalar and vector operators. Selection rules. Land\'e projection formula.

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

Atomic and molecular structure: Hydrogen atom; fine structure: relativistic corrections; spin-orbit coupling; hyperfine structure. Multi-electron atoms: LS coupling; Hund’s rules; Stark effect, 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.

Elements of quantum field theory: Quantization of the electromagnetic field, photons; number states. Radiative transitions, dipole approximation, selection rules, spontaneous emission and absorption, stimulated emission, Einstein’s A and B coefficients; Cavity rate equations and lasers, coherent states, non-classical light.

BOOKS

Quantum Physics, Gasiorowicz S (2nd edition, Wiley, 1996;  3rd edition, Wiley, 2003)

Quantum Mechanics, Commins E D (CUP, 2014)

Quantum Mechanics, Bransden B H and Joachain C J (2nd edition, Pearson, 2000)

Physics of Atoms and Molecules, Bransden B H and Joachain C J (2nd edition, Pearson, 2003)

The Principles of Quantum Mechanics Shankar R (2nd edition, Springer, 1994)

Problems in Quantum Mechanics, Squires G L (CUP, 1995)