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Stat mech: Fermi-Dirac distribution

  1. Mar 31, 2017 #1
    1. The problem statement, all variables and given/known data
    Show that the FD distribution can be viewed as giving the probability that a given state ( of the prescribed
    energy) is occupied.

    2. Relevant equations

    3. The attempt at a solution
    Solution to this problem:

    I understand the solution,but I took a different approach which gave a different answer.

    For a quantum state i,denote Z_i as its partition function.Then for a single state distribution(2nd red box) :

    For a fermion,n_i = 0 or 1. I want to find P(1) for the state i,so by the 2nd box it is P(1) = e^β(μ-ε_i) / Z_i , which is not the same as the FD distribution?
  2. jcsd
  3. Mar 31, 2017 #2


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    Staff: Mentor

    What happens if you multiply the numerator and the denominator by ##e^{-\beta (\mu - \epsilon)}##?
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