Advertisement

Quantum Mechanics of Identical Particles

  • Takafumi Kita
Part of the Graduate Texts in Physics book series (GTP)

Abstract

In general, superconductivity occurs in a system of identical particles; specifically, the conduction electrons in metals. Being indistinguishable from each other, swapping any two electrons leaves the system unchanged. This feature, which is associated with invariance under permutations, has a profound implication for every system composed of identical particles. We study a crucial connection between the spin of a particle and permutation symmetry of many-particle wave functions. We also develop a special technique called second quantization that enables us to describe such a system concisely and conveniently. The results are summarized generally in Sect. 3.7 and specifically for ideal gases in (3.61)–(3.65).

Keywords

Wave Function Coherent State Cyclic Permutation Identical Particle Slater Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    A.C. Aitken, Determinants and Matrices (Oliver and Boyd, Edinburgh, 1956)Google Scholar
  2. 2.
    A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957)MATHGoogle Scholar
  3. 3.
    M. Fierz, Helv. Phys. Acta 12, 3 (1939)CrossRefGoogle Scholar
  4. 4.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963)MathSciNetCrossRefADSGoogle Scholar
  5. 5.
    I.N. Herstein, I. Kaplansky, Matters Mathematical (Chelsea, New York, 1978)MATHGoogle Scholar
  6. 6.
    J.R. Johnston, Am. J. Phys. 38, 516 (1970)CrossRefADSGoogle Scholar
  7. 7.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd edn. (Butterworth-Heinemann, Oxford, 1991)Google Scholar
  8. 8.
    S. Lang, Linear Algebra (Springer, New York, 1987)CrossRefMATHGoogle Scholar
  9. 9.
    W. Pauli, Phys. Rev. 58, 716 (1940)CrossRefADSGoogle Scholar
  10. 10.
    J.J. Sakurai, Modern Quantum Mechanics, rev. ed. (Addison-Wesley, Reading, 1994)Google Scholar
  11. 11.
    E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)MathSciNetCrossRefADSMATHGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Takafumi Kita
    • 1
  1. 1.Department of PhysicsHokkaido UniversitySapporoJapan

Personalised recommendations