I Blochs theorem

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Bloch's theorem states that the wave functions for electrons in a periodic potential have the form:

ψn,k(r) = un(r)exp(ik⋅r)

, where un has the same periodicity as the potential.
Bloch's theorem is used to calculate energy bands, and my question is:
Does the n in un label the different bands of the crystal?
 

DrDu

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Yes, exactly
 
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Okay but if remember correctly then a band diagram can be constructed using an empty lattice approximation, where all wave vectors outside the Brillouin zone are mapped back into the Brillouin zone. In this case you get a band diagram, but the different bands need not necessarily belong to different n? or am I wrong? maybe I am mixing up different things.
 

DrDu

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Try to wrire down the u-n for the empty lattice.
 

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