**Foundations of Quantum Mechanics:**Operator methods. Observables. Resolution of the identity. Basis transformations. Position and momentum representations. Discrete and continuous spectra.**Quantum Dynamics:**Time development operator. Schrodinger, Heisenberg and interaction pictures. Canonical quantisation and constants of motion. The propagator. Introduction to path integral formulation.**Approximate Methods:**Variational methods and their application. The JWKB method and connection formulae, with applications to bound states and barrier penetration. The anharmonic oscillator.***Scattering Theory:**Scattering amplitudes and differential cross section. Partial wave analysis. Optical theorem. Green functions, weak scattering and the Born approximation. Beyond the Born approximation. Bound states.**Density Operators:**Pure and mixed states. The density operator and its properties. Time-dependence of the density operator. Applications in statistical mechanics. Density operator for subsystems. Quantum damping.*

The previous syllabus was:

**Introduction/Revision:**Mathematical foundations of non-relativistic quantum mechanics. Vector spaces. Operator methods for discrete and continuous eigenspectra. Generalized form of the uncertainty principle. Dirac delta function and delta-function potential.**Quantum Dynamics:**Time development operator. Schrodinger, Heisenberg and interaction pictures. Canonical quantisation and constants of motion. Coordinate and momentum representations. Free particle and simple harmonic oscillator propagators. Introduction to path integral formulation.**Approximate Methods:**Variational methods and their application to problems of interest. The JWKB method and connection formulae, with applications to bound states and barrier penetration. The anharmonic oscillator. Asymptotic expansions.**Scattering Theory:**Scattering amplitudes and differential cross section. Partial wave analysis and the optical theorem. Green functions, weak scattering and the Born approximation. Relation between Born approximation and partial wave expansions. Beyond the Born approximation.**Density Matrices:**Pure and mixed states. The density operator and its properties. Position and momentum representation of the density operator. Spin density matrix and polarisation. Density matrix for the harmonic oscillator. Applications in statistical mechanics.**Lie Groups:**Rotation group, SO(3) and SU(2). SO(4) and the hydrogen atom. Applications to atomic structure. SU(3) and quarks.

- (1) Removal of chapter on Lie Groups.
- (2) Additional material on strong scattering, bound states, density operator of subsystems, quantum damping.