Topics in Quantum Mechanics
This is an advanced course on quantum mechanics. It covers a wide range of topics, including an introduction to atomic physics, quantum foundations and scattering theory. (Some of these are taught as part of the Applications of Quantum Mechanics course in Cambridge.)
An expanded version of these notes has appeared as a textbook.
Discrete Symmetries
Parity; Time Reversal, Kramers' degeneracy.
Approximation Methods
The variational method; the helium atom; bound states, the Yukawa potential, the virial theorem; excited states. WKB, Semi-classical expansion, Linear potentials and the Airy function, Bohr-Sommerfeld quantisation, Tunnelling; The Sudden approximation, Quantum quenches; The Adiabatic approximation; Berry phase; The Born-Oppenheimer approximation, Molecular binding.
Atoms
Hydrogen; Spin-Orbit coupling, Fine structure, Hyperfine structure; Helium, Exchange energy; Hartree method, Slater determinant, Hartree-Fock method.
Atoms in Electromagnetic Fields
The Stark effect; The Zeeman effect; Rabi oscillations, Spontaneous emission, Selection rules, Photons, The Jaynes-Cummings model.
Quantum Foundations
Entanglement, The EPR paradox, Bell's inquality, CHSH inequality, GHZ states, The Kochen-Specker theorem; Entanglement is a resource, The CHSH game, Dense coding, Quantum teleportation, Quantum key distribution; Density matrices, The Bloch sphere, Entropy; Projective measurements, Generalised measurements; Open quantum systems, Decoherence, The Lindblad equation.
Scattering Theory
Scattering in one dimension, reflection and transmission coefficients, S-matrix, bound states, resonances; Scattering in three dimensions, the cross-section, the scattering amplitude, partial waves, phase shifts and the optical theorem, a hard sphere, bound states and resonances again; the Lippmann-Schwinger equation, the Born approximation, Yukawa and Coulomb potentials, the Born expansion; Rutherford scattering, the hydrogen atom; Scattering off a lattice, Bragg condition, structure factor, Debye-Waller factor.