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I am having trouble understanding some things about k-space or momentum space in a crystal. The trouble began when I was first introduced to the Bloch theorem, a few weeks back.

It is:

[tex]\psi_{n\mathbf{k}}(\mathbf{r})=e^{i\mathbf{k}\cdot\mathbf{r}}u_{n\mathbf{k}}(\mathbf{r}).[/tex]

In this equation, there is k, which is a vector in momentum space (?). Is it also a vector representing the quantum numbers? (i.e., are the momentum space vector components the quantum numbers of a particular solution of Schrodinger's equation?). Does this mean that in an E(k) plot, as you traverse a particular direction of k, you are traversing the quantum states of the system?

Also, the notation suggests that k is independent of r. In a crystal lattice with a periodic potential, if you move an electron around would not its momentum change also? I guess I'm not sure how the momentum and position of a particle in a crystal are independent of each other.

This MUST sound pretty vague, but there is something I'm not quite getting here. Thanks a lot for your help.

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# Momentum space

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