Quantum Leaps and Bounds: Quantum Mechanics in Fock Space

by

Malcolm McMillan, Department of Physics & Astronomy, University of British Columbia

This volume of QLB gives an introduction to the second-quantization description of nonrelativistic many-body systems. PDF file (193 pages) 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