Delocalization of electrons in metals Wikipedia defines a delocalized electron inside a metal as one that is free to move from one atom to another. This state of not being bound to any metal ion is what allows it to conduct electricity and so forth. But the delocalized electron which follows the Bloch wavefunction is evenly spread throughout the entire macroscopic crystal which means that a single electron can at one time be on end of the metal and in next instant be on the extreme other side.
How is it possible to define "movement" for such a situation where the electron being totally delocalized can pop up anywhere in the crystal at any time ?
The plane waves of a delocalized electron does not restrict its position to any localized region at all, then how is it correct to say that conduction happens because of delocalized electrons "moving" ? Dont you need something thats at least a tiny bit localized like a wavepacket inorder to define things like drift velocity etc ?
How can an electron with a Bloch wavefunction have a drift velocity or a mean path length thats only a few atoms long when the wavefunction is entirely spread throughout the metal ?
Shouldnt there be something that prevents an electron moving at some rate from randomly appearing millions of atoms away inorder to make quantities like mean path length sensible ?
Edit : as someone has rightly pointed out I seem to have posted too many questions and that too in a rather haphazard manner for which i apologize, but my main concern was arent scattering events which are important to defining say the relaxation time and other quantities themselves localized events ? So how can delocalized wavefunctions of electrons scatter at all while remaining in such a delocalized state ?
 A: Electrons are indistinguishable, they don’t have serial numbers or birthmarks or tattoos. There is an electron here now, and there was an electron way over there a split second ago. But there is no sense in which the electron here is the same individual electron as the electron there. (Also there is no sense that they are not the same)
When we talk about drift velocity we are not tracking the position of a single electron over time. What we are actually doing is closer to measuring the momentum at a single point and getting the speed from that. So there is no need to restrict or modify the wave function in the way you describe. The momentum is finite and hence the velocity and speed are also finite, regardless of the position that you measure.
Of course, in addition to the above, measuring the position would collapse the wavefunction to a different state anyway.
A: The short answer is that it is the wrong model to describe currents.
One critical assumption of the Bloch model is that we assume a periodic
potential with the same periodicity as the lattice itself. If we would apply a voltage on both ends of our solid body, that assumption wouldn´t hold anymore.
The reason why it is still useful for conduction phenomena is that it provides us with a tool to calculate the charge carrier density for a given crystal. This is what the ("stationary") energystructure also called bandstructure is used for. The charge carrier density can then be used for calculating the conductivity of the crystal.
