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. Familiarity and proficiency with the principles and methods of linear vector spaces is essential.
Learning Outcomes and Assessment
The course will build on PtIB Quantum Mechanics by revisiting certain topics in greater depth, and engaging with a new range of physical concepts and theoretical methods. A primary objective is to equip the student with a core package of analytical tools and to showcase their applications, with emphasis in atomic physics. These techniques will allow the student to comfortably enter more specialized courses in Part II and Part III. The course pays particular attention to perturbation theory, the relevance of symmetries and the introduction of elements of quantum field theory, through the quantisation of the electromagnetic field. Throughout the handouts, references will be made to valuable theorems and techniques so that the student has the key words necessary to seek further information, should they wish.
Synopsis
Review of Quantum Physics: Postulates of quantum mechanics, operator methods, time dependence. Solutions to the Schrödinger equation in one and three dimensions. The hydrogen atom. Angular momentum and spin; matrix representations. Addition of angular momentum, 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 charge particle in electromagnetic field: Gauge invariance; Aharonov-Bohm effect. Particle magnetic moments; Stern-Gerlach experiment. Landau levels, two-dimensional electron gas.
Symmetries: Translations and rotations, parity. Conservation laws. Wigner-Eckart theorem for scalar and vector operators. Selection rules. Landé projection formula.
Identical particles: Particle indistinguishability and quantum statistics; exchange interactions. The helium atom.
Atomic and molecular structure: The 'real' 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 perturbations: Transitions in two-level systems, Rabi oscillations; magnetic resonance. Spin transitions. Time-dependent perturbation theory, Fermi's Golden rule. Scattering, the Born approximation.
Elements of Quantum Field Theory: Quantization of the electromagnetic field, photons; number states. Radiative transitions, electric dipole approximation, selection rules, spontaneous emission and absorption, stimulated emission, Einstein's A and B coefficients; Cavity rate equations and lasers, coherent states.
References
Quantum Physics, Gasiorowicz S (2nd edition, Wiley, 1996; 3rd edition, Wiley, 2003)
Introduction to Quantum Mechanics, Griffiths D J and Schroeter D F (3rd edition, CUP, 2018)
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)
Principles of Quantum Mechanics Shankar R (2nd edition, Plenum, 1994)
Quantum Mechanics, Schwabl F (4th edition, Springer, 2007)