Advanced Quantum Mechanics

My fourth-year 10-credit course Advanced Quantum Mechanics, last given in 2019/20, was part of the 20-credit module Advanced and Further Quantum Mechanics. Indicative syllabus of my course:

• Time-dependence: Brief review of time-dependent Schrödinger equation; stationary states; time-evolution of general wavefunctions; time evolution operator; time-energy uncertainty relation. Time-dependent perturbation theory. Fermi's golden rule; selection rules for atomic transitions re-examined. Ehrenfest’s theorem.
• The classical limit: Classical mechanics of particles as a limit of quantum mechanics, mostly studied through wavepacket motion.
• Many-particle systems: Identical particles and exchange symmetry, fermions and bosons, the Pauli Principle; use of Slater determinants. Variational principle for many-electron systems; the Hartree and Hartree-Fock approximations. Density-functional theory and the local-density approximation.
• Second quantisation: Creation, annihilation and number operators; their use for many-particle systems; anti-commutation relations; field operators; Heisenberg picture. Introduction to many-body perturbation theory. Introduction to quantisation of the electromagnetic field.

Outline notes for the course

Rex's interactive geogebra.org demonstrations for this course are publicly available:

• Time evolution of a harmonic oscillator
• Wavepacket dynamics
• Fermi's Golden Rule

From 2020/21, Advanced Quantum Mechanics is taught by Dr Aries Ferreira.

Rex Godby