When we talk about current, we say electrons are "flowing" through a conductor. But if electrons are identical particles, how does it make sense to talk about them flowing?
To expand on that: imagine the simplest wire, just a 1-D chain of copper atoms, each with one conduction electron. If we apply a potetntial across the wire, what happens? Of course, we say there is a current, and the electrons "flow". But what does that really mean?
Suppose when the electrons "flow", each copper atom gives its electron to the next atom in the line. From a QM perspective, nothing has changed! The 'before' wave function is identical to the 'after' wave function, because all that we have done is exchange particles, and the wavefunction has to be symmetric upon particle exchange. The state of the system before and after the "flow" occured is exactly the same. So what does it really mean to say that there is a current flowing?