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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.

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# Homework Help: Statistical Physics: Partition function and fermions

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