- Title Pages
- Dedication
- Preface
- 1 Schrödinger equation on a lattice
- 2 Dirac notation
- 3 Back to the Schrödinger equation on a lattice
- 4 Operator mechanics
- 5 Time evolution and wavepackets
- 6 Simultaneous observables
- 7 Continuity equation and wavefunction properties
- 8 Bound states in one dimension
- 9 Scattering in one dimension
- 10 Periodic potentials
- 11 The harmonic oscillator
- 12 WKB approximation
- 13 Quantum mechanics and path integrals
- 14 Applications of path integrals
- 15 Angular momentum
- 16 Bound states in spherically symmetric potentials
- 17 The hydrogen-like atom
- 18 Angular momentum and spherical symmetry
- 19 Scattering in three dimensions
- 20 Time-independent perturbation expansion
- 21 Applications of perturbation theory
- 22 Time-dependent Hamiltonian
- 23 Spin angular momentum
- 24 Adding angular momenta
- 25 Identical particles
- 26 Elementary atomic physics
- 27 Molecules
- 28 The elasticity field
- 29 Quantization of the free electromagnetic field
- 30 Interaction of radiation with charged particles
- 31 Elementary relativistic quantum mechanics
- Appendix A Review of the Dirac delta function
- Appendix B Normalization integral of spherical harmonics
- Appendix C Legendre equation
- Appendix D Expression for the spherical Bessel function
- Index

# Identical particles

# Identical particles

- Chapter:
- (p.236) 25 Identical particles
- Source:
- Practical Quantum Mechanics
- Author(s):
### Efstratios Manousakis

- Publisher:
- Oxford University Press

This chapter discusses the case of a many-body system of identical particles. It considers the consequencies of the symmetry of the Hamiltonian under particle permutations in this case. It discusses how to build many-body Boson and Fermion states. It then introduces the formalism of so-called second quantization, which is usefu, in the case of identical particles. It also expresses the many-body Hamiltonian in terms of creation and annihilation operators.

*Keywords:*
identical particles, Fermions, Bosons, Slater determinants, second quantization, creation operators, annihilation operators

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- Title Pages
- Dedication
- Preface
- 1 Schrödinger equation on a lattice
- 2 Dirac notation
- 3 Back to the Schrödinger equation on a lattice
- 4 Operator mechanics
- 5 Time evolution and wavepackets
- 6 Simultaneous observables
- 7 Continuity equation and wavefunction properties
- 8 Bound states in one dimension
- 9 Scattering in one dimension
- 10 Periodic potentials
- 11 The harmonic oscillator
- 12 WKB approximation
- 13 Quantum mechanics and path integrals
- 14 Applications of path integrals
- 15 Angular momentum
- 16 Bound states in spherically symmetric potentials
- 17 The hydrogen-like atom
- 18 Angular momentum and spherical symmetry
- 19 Scattering in three dimensions
- 20 Time-independent perturbation expansion
- 21 Applications of perturbation theory
- 22 Time-dependent Hamiltonian
- 23 Spin angular momentum
- 24 Adding angular momenta
- 25 Identical particles
- 26 Elementary atomic physics
- 27 Molecules
- 28 The elasticity field
- 29 Quantization of the free electromagnetic field
- 30 Interaction of radiation with charged particles
- 31 Elementary relativistic quantum mechanics
- Appendix A Review of the Dirac delta function
- Appendix B Normalization integral of spherical harmonics
- Appendix C Legendre equation
- Appendix D Expression for the spherical Bessel function
- Index