1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    Q.jpg

    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) :
    F.jpg

    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

    DrClaude

    User Avatar

    Staff: Mentor

    What happens if you multiply the numerator and the denominator by ##e^{-\beta (\mu - \epsilon)}##?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Stat mech: Fermi-Dirac distribution
Loading...