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Homework Help: Statistical Physics: Partition function and fermions

  1. Dec 31, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    The partition function for fermions is (according to Wikipedia: http://en.wikipedia.org/wiki/Partit...hanics)#Relation_to_thermodynamic_variables_2) given by:

    [tex]
    Z = \prod\limits_i {\left( {1 + \exp \left[ { - \beta \left( {\varepsilon _i - \mu } \right)} \right]} \right)},
    [/tex]

    where the product is over the different states. I cannot see how this works out correct:

    Let's look at a system with 3 single-particle (energi 0, 1 and 2) states with two fermions. Each fermion can be in one state, so there is a total of 3 states. Using the above expression this should give us

    [tex]
    Z = \left( {1 + \exp \left[ { - \beta \left( {(0 + 1) - \mu } \right)} \right]} \right)\left( {1 + \exp \left[ { - \beta \left( {(0 + 2) - \mu } \right)} \right]} \right)\left( {1 + \exp \left[ { - \beta \left( {(1 + 2) - \mu } \right)} \right]} \right).
    [/tex]

    Have I understood this correctly?

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
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