9 March 2014
If you open a good quantum mechanics text, you will likely find a section on how one models systems of identical particles in quantum mechanics. In particular, you should find the statement of a certain postulate that sums up how this is done. It's called the symmetrization postulate. Understanding this postulate, and therefore understanding how to deal with identical particles in quantum mechanics, hinges on an understanding of what it means to permute particles in quantum mechanics.
In this article, we show what it mathematically means to act on a quantum system with a permutation. Along the way, we introduce some useful mathmatical concepts: the permutation group of a set, and group actions. We illustrate all of the concepts with concrete examples involving simple quantum systems.