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.
General
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 (18003865656)). 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 21.121.3 (algebra of operators)
 Ballentine Chap 17 (symmetry of wavefunction)

 (Aside: spin and statistics:
handwavy proof
and The rigorous book)
 Reif 9.49.7 (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.477478
(scattering cross sections, rotational lines)
 Sakurai Modern QM 6.5 (Young Tableaux)
 Young Diagrams,
Particle Data Group (at LBNL)
 Merzbacher 21.46 (2nd quantization)
 Baym eqn. 1931 ff. (momentum basis), 1956 ff. KE operator, correlation
functions (1 and 2 particle)
 Hatfield, eqn 2.56 ff (locality discussionfind the bug here if you
want!)
 Applications
 Baym, 1994 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 2018 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 BoseEinstein 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 2.12.4, 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. 546548 (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 1720 (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, 2.12.2 (Quantizing EM field)
 For more information on gauge fixing and A_{0} 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 234 (interaction with a current)

Murayama's notes (same as above), pages 58.
 Itzykson & Zuber p. 138141 or Ballentine p. 535539 (Vacuum energy and
Casimir Effect)
 Relativistic Quantum Mechanics and Quantum Field Theory
 Ramond 1.2, 1.3 (Lorentz and Poincare group)
 Baym p. 499504 (KleinGordon Field)
 Also see for the KG equation these
Notes by D. Gingrich
 Sakurai 31 (probability and KG field)
 Mandl and Shaw 32 (Complex scalar field quantization)
 Mandl and Shaw p. 73 (spinstatistics comments)
 Sakurai 32 (Derivation of Dirac equation)
 Merzbacher 242 (Dirac equation, our gamma matrix conventions!),
also see Mandl and Shaw 42 and these
notes
on Dirac equation by D. Gingrich
 Mandl and Shaw pp.6367, 334339 and/or
Sakurai 8384 and 9194 (Basis functions for Dirac equation, Lorentz
transformations, helicity)
 Mandl and Shaw 43 (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 45 (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 138139 (rates in terms of matrix elements)
 Sakurai, beginning of 42 (brief description of Smatrix theory)
 Mandl and Shaw 62,63 (also brief description of Smatrix 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.
