Advanced Quantum Mechanics
Information for students taking the fourthyear 10credit course Advanced Quantum Mechanics (part of the 20credit module Advanced and Further Quantum Mechanics) is now provided through the Yorkshare VLE.
Indicative syllabus:

Timedependence: Brief review of timedependent Schrödinger equation; stationary states; timeevolution of general wavefunctions; time evolution operator; timeenergy uncertainty relation. Timedependent perturbation theory. Fermi's golden rule; selection rules for atomic transitions reexamined. Ehrenfest’s theorem.

The classical limit: Classical mechanics of particles as a limit of quantum mechanics, mostly studied through wavepacket motion.

Manyparticle systems: Identical particles and exchange symmetry, fermions and bosons, the Pauli Principle; use of Slater determinants. Variational principle for manyelectron systems; the Hartree and HartreeFock approximations. Densityfunctional theory and the localdensity approximation.

Second quantisation: Creation, annihilation and number operators; their use for manyparticle systems; anticommutation relations; field operators; Heisenberg picture. Introduction to manybody perturbation theory. Introduction to quantisation of the electromagnetic field.
Rex Godby