# David Tong: Lectures on 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. Please do email me if you find any typos or mistakes.

PostScript
PDF

Cambridge students: Lecture notes for the Part II course Applications of Quantum Mechanics
can be found here.

# Content

**1. Discrete Symmetries: PDF**

Parity; Time Reversal, Kramers' degeneracy.**2. Approximation Methods: PDF**

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.**3. Atoms: PDF**

Hydrogen; Spin-Orbit coupling, Fine structure, Hyperfine structure; Helium, Exchange energy; Hartree method, Slater determinant, Hartree-Fock method.**4. Atoms in Electromagnetic Fields: PDF**

The Stark effect; The Zeeman effect; Rabi oscillations, Spontaneous emission, Selection rules, Photons, The Jaynes-Cummings model.**5. Quantum Foundations: PDF**

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.**6. Scattering Theory: PDF**

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.

# Problem Sheets

(for the Applications of Quantum Mechanics course.)

**Problem Sheet 1: Postscript PDF**Scattering**Problem Sheet 2: Postscript PDF**Variational Method, 1d Band Structure**Problem Sheet 3: Postscript PDF**3d Band Structure; Fermi Surfaces**Problem Sheet 4: Postscript PDF**Phonons; Particles in a Magnetic Field**Notes on Spherical Bessel Functions: Postscript PDF**

# Quantum Mechanics on the Web

**Applications of Quantum Mechanics**An earlier version of this course by Ron Horgan**Quantum Mechanics**by Robert Littlejohn at Berkeley**Advanced Quantum Mechanics**by Ben Simons in TCM, Cambridge**Quantum Information**by John Preskill at Caltech