# Statistical Physics: Partition function and fermions

1. Dec 31, 2008

### Niles

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:

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

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

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

Have I understood this correctly?