Change in Syllabus 2020/21
The new syllabus in 2020/21 is:
- Quantum Dynamics
Schrodinger, Heisenberg, interaction picture.
The evolution operator and time ordering.
Driven oscillator. Coherent states.
A spin-$\frac{1}{2}$ in a field.
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 $SL(2,\mathbb{C})$.
- Relativistic Quantum Physics
Klein-Gordon equation. Antiparticles.
Spinors and the Dirac equation. Relativistic covariance.
(Italicized items are not for examination.)
The changes are:
- (1) Addition of JWKB.
- (2) Quantum damping made examinable.