# Electrons moving due to a field

I am trying to understand what happens to the electrons in a solid when I apply a field. If I consider the free electron model at 0 K, I have a Fermi sphere and only those electrons at the Fermi energy have empty states which they can access. Then it is these electrons that are able to respond to the field and transition between discrete momentum states, closely spaced in energy, as they accelerate. Stop me if any of this sounds wrong.

So that's fine. But of course in my semi-classical view, I am picturing an electron as a particle which is accelerating towards one end of the crystal due to the field. I'm having trouble reconciling this real space picture with the k-space picture of Fermi surfaces and momentum states. The states that the electron occupies in k-space say nothing about the particle's position in the crystal, they only relate its momentum (as a wave) to its energy. In fact, as my professor said in passing, there is no position information because all the electrons already sample the entire crystal. I take this to mean that the state of the electron gives some probability distribution over the whole crystal, with an associated momentum and energy. But then, what does it mean for the electron to move in response to the field? Is it true that the states which I am assigning it to in k-space don't allow for a localized position in the crystal? In that case, I would assume that I need to construct new states for this system of crystal + field, which allow for an asymmetric probability distribution of the electrons. But it can't be the case that the states of all the particles completely change simply due to a small field.

You'll have to bear with me. I'm trying to interpret this material using my limited knowledge of quantum mechanics.

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I thought about it more, and I guess it's not such a hard question. Of course the states of the particle completely change; that's what you do in perturbation theory, you calculate the change in the wavefunctions. Even if the field is just a perturbation you still fundamentally change the states...

ZapperZ
Staff Emeritus