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Band structure a result of Pauli ? Professor hopelessly vague or in essence correct?

  1. Feb 16, 2012 #1
    "Band structure a result of Pauli"? Professor hopelessly vague or in essence correct?

    Hello,

    I'm taking an introductory course on Solid State physics (level: last year undergrad physics) and the professor said one can view the band structure in solids as a result of the Pauli principle, since the valence electrons can occupy the same "place", and hence must have different energies to fullfill the Pauli principle. I objected in class (politely, in the format of a question) that Pauli didn't require different energies, but merely different states and reminded him of degeneracies (although in the back of my mind I was struggling with more of what he said, this was what struck me the most), upon which he responded with something along the lines of "indeed that is also possible, but if one is thinking about free electrons in a box, then if we ignore the spin variable part, different electrons have different energies". I don't really get what he's saying; aren't there degeneracies in the free electron gas? And anyway, he afterwards specified that his intuitive view was related to the tight binding method, also known as LCAO (linear combination of atomic orbitals), however this seems to be a long way from free electron gases (which he used in his argumentation).

    In short, I would suspect that it's impossible to get something coherent out of it, but on the other hand I don't want to be rash and although my experimental physics professors are often very vague, I'm also willing to believe that somewhere tucked away in his obscure explanation, is a core of truth. Can anybody find it? Am I right in being confused about what he said? (note: I'm not posting this to vent, at all! My main intention is to simply understand what he meant)
     
  2. jcsd
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