Theoretical Physics 2 (2009-10)

• 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.
• Approximation 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 Matrices: 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*.

Lecture Notes and Examples Errata --> Solutions to Problems

Past Exam Papers 2008 [pdf], answers [pdf] N.B. Syllabus changed in 2007/8. [Details] 2007 [pdf], answers [pdf] 2006 [pdf], answers [pdf] 2005 [gz-ps,pdf], answers [gz-ps,pdf] N.B. Syllabus changed in 2004/5. [Details] 2004 [gz-ps,pdf], answers [gz-ps,pdf] 2003 [gz-ps,pdf], answers [gz-ps,pdf] 2002 [gz-ps,pdf], answers [gz-ps,pdf] 2001 [pdf] 2000 [gz-ps,pdf] 1999 [gz-ps,pdf] 1998 [gz-ps,pdf] 1997 [pdf] 1996 [pdf]