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.
Content
- 1. Discrete Symmetries:
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Parity; Time Reversal, Kramers' degeneracy. - 2. Approximation Methods:
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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:
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Hydrogen; Spin-Orbit coupling, Fine structure, Hyperfine structure; Helium, Exchange energy; Hartree method, Slater determinant, Hartree-Fock method. - 4. Atoms in Electromagnetic Fields:
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The Stark effect; The Zeeman effect; Rabi oscillations, Spontaneous emission, Selection rules, Photons, The Jaynes-Cummings model. - 5. Quantum Foundations:
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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:
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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 
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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