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Bloch theorem?

  1. Sep 25, 2009 #1
    Hi guys I have these question, please someone help me to answer?
    What is Bloch theorem? Why we use it? Explain?
    What is the consequence of this theorem?
  2. jcsd
  3. Sep 25, 2009 #2
    The Bloch theorem allows us to partially diagonalize a periodic Hamiltonian. A periodic Hamiltonian has a discrete translational symmetry, you can translate by any lattice vector and get the same Hamiltonian back. Because of this symmetry, there will be a good quantum number for the wavefunction associated with it, usually called the pseudomomentum and given the letter k. This allows us to take a problem of N atoms in M cells and solve M independent problems with N atoms, rather than to solve the whole crystal of N*M atoms. The consequences of Bloch's theorem are pervasive in solid-state physics, so it is difficult to give a concise summary.
  4. Sep 25, 2009 #3
    Thank you for your response.
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