Quantum Leaps and Bounds: Quantum Mechanics in Fock Space

by

Malcolm McMillan, Department of Physics, University of British Columbia

Quantum Leaps and Bounds (QLB) is the six-volume set of lecture notes in book form for Physics 500, the introductory graduate quantum mechanics course given by Malcolm McMillan at UBC at various times since 1973.

This volume of QLB gives an introduction to the second-quantization description of nonrelativistic many-body systems. The table of contents of this volume is:

Introductory Remarks
n-particle System
- n distinguishable particles; permutation operators
- n identical particles; invariance of observables; symmetry of states
Occupation Number Representation
- System of identical fermions; Slater determinants
- System of identical bosons
- System of identical fermions and bosons
Fock Space for Fermions: Part 1
- Fermion Fock space defined
- Creators and annihilators; anticommutation relations
- Number operators
- Observables; one- and two-particle operators
- Hamiltonian
- Independent-particle model; Hartree-Fock potential
- Particle-hole states
- Correlated particle-hole model; quasiparticles; quasiholes
Fock Space for Fermions: Part 2
- Quantum field operator
- Momentum/spin operator
- Momentum/helicity operator
- Hamiltonian
Fock Space for Bosons
- Boson Fock space defined
- Creators and annihilators; commutation relations
- Quantum field operator
- Momentum/spin and momentum/helicity operators
Fock Space for Fermions and Bosons
- Fundamental dynamical variables
- Trilinear interaction
- Dressing transformation
- Dressing the trilinear interaction; Yukawa potential
Appendix A: Two Distinguishable Particles
Appendix B: Three Distinguishable Particles
Appendix C: Some Commutators