# Does the “particle exchange” operator have any validity?

In introductory quantum mechanics books the topic of identical particles often introduces a "particle exchange" operator. This operator, when applied to a multi-particle wave-function, exchanges the positions of two identical particles.

However, it seems to me that this is a non-physical thing. Particles can't really "exchange positions" can they? Does such an operator really have validity?

You've already seen this attitude earlier in quantum mechanics. For example, the position operator $$\hat{x}$$ is not a "physical thing", in the sense that if you have a state $$|\psi \rangle$$, $$\hat{x} |\psi \rangle$$ is not necessarily a sensible physical state. Instead $$\hat{x}$$ is useful because it represents an observable quantity. In quantum mechanics, operators are our basic tools. Some represent observables, some represent physical time evolutions, and some represent neither, and there's nothing wrong with those last ones.