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I Blochs theorem

  1. Apr 29, 2016 #1
    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?
     
  2. jcsd
  3. Apr 29, 2016 #2

    DrDu

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    Yes, exactly
     
  4. Apr 29, 2016 #3
    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.
     
  5. Apr 29, 2016 #4

    DrDu

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