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If we have a free electron with a certain wavenumber k, then this is equivalent to the momentum of the particle since [itex]p=\hbar k[/itex]. For an electron in a Bloch state, this is not the case. Apparently k is not the momentum of the electron. But what is the physical meaning of k for a Bloch state then ? Can I think of k as telling me the direction in which the electron is moving?

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# Bloch state wave vector

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