Theoretical Physics 2 - Lent 2023
This is the course website for Theoretical Physics II. Relevant information will be posted here and on the online system.

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.

Course content
Handout with problem sets can be found here

Past exams
to be posted


Time table and class hours
TP2 is scheduled for Monday and Wednesday at 14:00 in the Pippard Lecture Theatre, starting on Monday 22th January and finishing on the 14th of March. Examples Classes are scheduled at the same slot on Tuesdays at 14:00 in the Pippard Lecture Theatre, starting on January 30 (alternating weeks, finishing on the 13th of March).

Books
  • Modern Quantum Mechanics, Sakurai J J (2nd edn Addison-Wesley 1994)
  • (Advanced) Quantum Mechanics, Schwabl F (4th edn Springer 2007/2008)
  • Principles of Quantum Mechanics, Shanker R (2nd edn Springer 1994)
  • Lectures on Quantum Mechanics, Baym G (Benjamin WA 1969)
  • For mathematical background we heartily recommend Mike Stone and Paul Goldbart’s Mathematics for Physicists: A guided tour for graduate students (SUP, 2009). This contains a lot of advanced material as well as much of what you covered in IB Mathematics.
  • A great resource for just about anything you may need to know about any of the functions we meet is the NIST Digital Library of Mathematical Functions at http://dlmf.nist.gov.