Quantum Mechanics of Identical Particles
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).
KeywordsWave Function Coherent State Cyclic Permutation Identical Particle Slater Determinant
- 1.A.C. Aitken, Determinants and Matrices (Oliver and Boyd, Edinburgh, 1956)Google Scholar
- 7.L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd edn. (Butterworth-Heinemann, Oxford, 1991)Google Scholar
- 10.J.J. Sakurai, Modern Quantum Mechanics, rev. ed. (Addison-Wesley, Reading, 1994)Google Scholar