David Tong: Topics in Quantum Mechanics

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.


  • 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