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Question about Bloch function in Reduced Zone Scheme

  1. Jan 12, 2013 #1
    The classical textbook, Introduction to solid state physics by Charles Kittle said:
    "If we encounter a Bloch function written as [tex]ψ_{k’}(r)=exp(i{k’}r) u_{k’}(r)[/tex], with k’ outside the first zone, we may find a suitable reciprocal lattice vector G such that k=k’+G lies within the first Brillouin zone. Then
    [tex]ψ_{k’}(r)=exp(ik’r) u_{k’}(r)=exp(ikr) [exp(-iGr) u_{k’}(r)][/tex]
    [tex]=exp(ikr) u_k(r)=ψ_k(r)[/tex]"
    I wonder why [tex]exp(-iGr) u_{k’}(r)=u_k(r)[/tex], how to derive this relation?
     
    Last edited: Jan 12, 2013
  2. jcsd
  3. Jan 12, 2013 #2
    He probably defines [itex]u_k(r)[/itex] this way. It is just the old u times a complex phase.
     
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