Quantum Mechanics


Posted here are my notes for a course in quantum mechanics at the graduate level. I will update these notes regularly and put corrections in as I find them, and you can always contact me if you have corrections or comments.



You can download the notes here as one big file: (pdf, many MB). Instructors may contact me for a version with solutions to problems included.



If you use these notes for your class, please let me know!



Topics Covered:

  1. Classical Mechanics: Review of variational principles
  2. Axioms of Quantum Mechanics: Hilbert spaces, time evolution, quantization, representations, unitarity
  3. Basic Examples: Free particle, infinite and finite square wells, square barriers, tunneling and reflection
  4. Double-Well Potential: tunneling/Rabi oscillations, quantum Zeno effect, avoided crossings, adiabatic passage
  5. Harmonic Oscillator: Ladder operators, coherent states, classical limit
  6. Semiclassics: Ehrenfest equations, standard quantum limit, WKB approximation
  7. Angular Momentum: ladder operators, addition, rotations, irreducible tensor operators, Wigner-Eckart theorem, multipole radiation
  8. Three-Dimensional Particles: Free particle, hydrogen atom
  9. Spin: Bloch sphere, precession, entanglement, EPR paradox, Bell theorem
  10. Multiple Particles: Density operator, entanglement, cloning, teleportation, indistinguishability
  11. Time-Independent Perturbation Theory: Resolvent operator, Stark effects, degeneracy, fine structure, hyperfine structure, Zeeman effect
  12. Time-Dependent Perturbation Theory: Dyson series, Green functions, Rabi oscillations, rotating-wave approximation, Bragg diffraction, ac polarizability
  13. Linear-Response Theory: Kubo formula, causality, fluctuation-dissipation theorem, Johnson noise
  14. Continuum Transitions: Fermi golden rule, spontaneous decay, photoionization
  15. Path Integration: propagator, functional integration, classical limit, Gel'fand-Yaglom method, van Vleck-Morette determinant