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Homework Help: Two energy level system calculate average occupancy

  1. Dec 14, 2016 #1

    I need help with the following question:
    A system has two energy levels, ε and ε1 that can be occupied by fermions (spin=1/2) that are non-interacting from a reservoir at temperature T and chemical potential μ. Compute the avarage occupation number of the state with energy ε.

    I have written down the grand canonical partition function and it is (1+e^(-β(ε-μ))^2)((1+e^(-β(ε1-μ)))^2)

    and I know the formula for avarage occupation number for fermions is
    ΣnP(n) where n goes from 0 to 1.

    But then I'm stuck. The hint I got was that there can be up to four particles and there are different possibilities to put these into the energy levels.

    Very thankful for any help!
  2. jcsd
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