Expectation value of velocity of Bloch electrons ↩

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created: 2022-02-23 16:17:28
modified: 2022-02-23 16:35:15

From Bloch's theorem, we know that the eigenstates of particles are of the following form in a lattice periodic potential:

Where has the same periodicity as the potential.

We can simplify the expectation value of the velocity operator on these states¹:

So this way we essentially have a new operator that acts on and not on the whole wave function.