Physics 221b:
Graduate Quantum Mechanics II
Reading References

This has both source material for lectures and pointers to some more in depth discussion than needed for this class.


Books for the class include:
  • Merzbacher, Quantum Mechanics, 3rd edition
  • recommended: Sakurai, Advanced Quantum Mechanics
  • recommended: Ballentine, Quantum Mechanics
  • recommended: Baym, Lectures on Quantum Mechanics (might find here or call Westview Press (1-800-386-5656)). There is a 20% discount if you order from the press, so I recommend that route!
  • recommended: Mandl and Shaw, Quantum Field Theory
  • also see:
    • Sakurai, Modern Quantum Mechanics
    • Hatfield, Quantum Field Theory of Point Particles and Strings
    • Fradkin, Field Theories of Condensed Matter Systems
    • Fetter and Walecka, Quantum Theory of Many Particle Systems
    • Wilczek, Fractional Statistics and Anyon Superconductivity
    • Jackson, Classical Electrodynamics
    • 221B homepage from 2002
    • Itzykson and Zuber, Quantum Field Theory
    • Online Lecture notes, for Klein Gordon and Dirac equations, by D. Gingrich
    • Ramond, Field Theory, A modern Primer
    • A. Zee, Quantum Field Theory in a Nutshell

In order covered in lecture (topic in parentheses)

  • Identical Particles
    • Merzbacher 10.6 (beginning, harmonic oscillator review)
    • Merzbacher 21.1-21.3 (algebra of operators)
    • Ballentine Chap 17 (symmetry of wavefunction)
      (Aside: spin and statistics: hand-wavy proof and The rigorous book)
    • Reif 9.4-9.7 (statistics)
    • Normalization of fermionic wavefunction in terms of one particle states.
    • Merzbacher 18.8, Sakurai Modern QM 6.3,6.4 (He atom)
    • Baym chap 18, Ballentine pp.477-478 (scattering cross sections, rotational lines)
    • Sakurai Modern QM 6.5 (Young Tableaux)
    • Young Diagrams, Particle Data Group (at LBNL)
    • Merzbacher 21.4-6 (2nd quantization)
    • Baym eqn. 19-31 ff. (momentum basis), 19-56 ff. KE operator, correlation functions (1 and 2 particle)
    • Hatfield, eqn 2.56 ff (locality discussion--find the bug here if you want!)
  • Applications
    • Baym, 19-94 ff. (Pert. of many body ground state/corrln function)
    • Merzbacher 22.1,22.2 (Angular Momentum)
    • Merzbacher 2nd edition! 21.3 (spin waves)
    • Merzbacher 22.5 (Quantum Stat Mech)
    • Baym eqn 20-18 ff. (Hartree and Thomas Fermi approximations)
    • Merzbacher 22.4, Ballentine 18.2 (Hartree Fock)
    • Ballentine 18.3 (Criticisms of Hartree Fock)
    • Chapter 3 of this thesis for more on Bose-Einstein Condensates
    • Fetter and Walecka, sec 41 (Independent pair model, more detail than we'll do, they do many examples)
      • Notes on the independent pair approximation.
    • Fradkin 2.1-2.4, 3.1 (Hubbard Model, strong and weak coupling)
      • How to get from eqn. 2.3.12 to 2.3.13 in Fradkin's book
    • Baym Ch. 8 (pairing interaction in superconductivity), see also (instead?) these lectures
    • Ballentine 18.5 (BCS vacuum and Bogoliubov transformations)
    • Merzbacher,2nd ed p. 546-548 (difference between normal and BCS ground state energies in detail)
    • See also for more discussion, J. Moore's lecture notes:
    • General comments, props of states, and a summary of points about BCS .
    • (Aside, for further examples: Birrell and Davies, Quantum fields in curved space, secs 3.2, 3.3, Bogoliubov transformations in general relativity)
    • Wilczek, p4 and p 17-20 (anyons)
  • Photons and the electromagnetic field
    • Jackson 11.9 (Field equations and gauge potentials)
    • Also see Murayama's notes from 221b in the past for much of this.
    • Mandl and Shaw 1.1 and 1.2 (Quantizing EM field)
    • Sakurai, 2.1-2.2 (Quantizing EM field)
      • For more information on gauge fixing and A0 see for example, Field Theory: A modern primer, by Ramond, section 7.1.
    • Sakurai, 2.3 (Classical vs. Quantum properties)
    • Sakurai, 2.4 (Interactions with matter)
    • Mandl and Shaw pages 13,14 and 19 (interactions with matter)
    • Mandl and Shaw 1.4.4 or Sakurai p 51 (Thomson scattering)
    • Merzbacher 23-4 (interaction with a current)
    • Murayama's notes (same as above), pages 5-8.
    • Itzykson & Zuber p. 138-141 or Ballentine p. 535-539 (Vacuum energy and Casimir Effect)
  • Relativistic Quantum Mechanics and Quantum Field Theory
    • Ramond 1.2, 1.3 (Lorentz and Poincare group)
    • Baym p. 499-504 (Klein-Gordon Field)
      • Also see for the KG equation these Notes by D. Gingrich
    • Sakurai 3-1 (probability and KG field)
    • Mandl and Shaw 3-2 (Complex scalar field quantization)
    • Mandl and Shaw p. 73 (spin-statistics comments)
    • Sakurai 3-2 (Derivation of Dirac equation)
    • Merzbacher 24-2 (Dirac equation, our gamma matrix conventions!), also see Mandl and Shaw 4-2 and these notes on Dirac equation by D. Gingrich
    • Mandl and Shaw pp.63-67, 334-339 and/or Sakurai 83-84 and 91-94 (Basis functions for Dirac equation, Lorentz transformations, helicity)
    • Mandl and Shaw 4-3 (Quantizing Dirac equation)
    • See also the books by Halzen and Martin and the book by Griffiths on particle theory for other ways of introducing this material.
    • Mandl and Shaw 4-5 (Gauge invariance)
    • Mandl and Shaw 8.1, 8.2 and 11.5 (rates, cross sections and spin sums) (Sakurai also does this but because of his funny metric, things look a bit different along the way)
    • Mandl and Shaw 138-139 (rates in terms of matrix elements)
    • Sakurai, beginning of 4-2 (brief description of S-matrix theory)
    • Mandl and Shaw 6-2,6-3 (also brief description of S-matrix theory)
    • Zee, Chapter 3 (renormalization), Ramond, Chapter 4 (for a scalar field theory): both a lot of useful detail, Zee is more about the ideas, Ramond more about how to do it.

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