Theoretical Physics 2 (2020/21)

Synopsis

Quantum Dynamics
Schrödinger, Heisenberg, interaction picture. The evolution operator and time ordering. Driven oscillator. Coherent states. A spin-1/2 in a field. Rabi oscillations. The adiabatic approximation. Landau-Zener transitions. Berry's phase.
Introduction to path integrals
The propagator and the Green's function: free particle and harmonic oscillator. The method of stationary phase, the JWKB method and the semiclassical limit.
Scattering Theory
Scattering in one dimension. Scattering amplitude and cross section. Optical theorem. Lippmann-Schwinger equation. Born series. Partial wave analysis. Bound states.
Identical Particles in Quantum Mechanics
Second quantisation for bosons and fermions. Single-particle density matrix and density-density correlation function. Bose-Hubbard model. Bogoliubov transformation. Interference of condensates.
Density Matrices
Density matrix and its properties. Applications in statistical mechanics. Density operator for subsystems and entanglement. Quantum damping.
Lie Groups
Symmetries are groups. Lie algebra of generators. Rotations as Lie group. Representations of SO(3), SU(2), Lorentz group SO(1,3) and SL(2,C).
Relativistic Quantum Physics
Klein-Gordon equation. Antiparticles. Spinors and the Dirac equation. Relativistic covariance.
[Topics in italics are non-examinable.]

Lecture Notes and Examples

Handout [pdf]
Errata

Selected Solutions to Examples

Appendix A, Chapters 1 and 2 [pdf]
Chapters 3 and 4 [pdf]
Chapters 5, 6 and 7 [pdf]
[Further notes on Landau-Zener tunneling and Problem 5.5.]

Lecture recordings, and slides from the lectures will be made available on Moodle.

Answers to email queries.

Examples Classes

All registered students can access the online sessions via the MSTeams group. Link available on Moodle.

2 Feb, 2pm-4pm

16 Feb, 2pm-4pm

2 Mar, 2pm-4pm

16 Mar, 2pm-4pm

Past Exam Papers

2021 [pdf], answers [pdf]
N.B. Syllabus changed in 2020/21. [Details]
2020 [pdf], answers [pdf]
N.B. Syllabus changed in 2019/20. [Details]
2019 [pdf], answers [pdf]
2018 [pdf], answers [pdf]
2017 [pdf], answers [pdf]
2016 [pdf], answers [pdf]
2015 [pdf], answers [pdf]
2014 [pdf], answers [pdf]
2013 [pdf], answers [pdf]
N.B. Syllabus changed in 2012/13.
2011 [pdf], answers [pdf]
2010 [pdf]
2009 [pdf], answers [pdf]
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]