# Partition function

1. Apr 11, 2008

### Pacopag

1. The problem statement, all variables and given/known data
If we have a system of N independent particles and the partition function for one particle is Z_1, then is the partition function for the N particle system Z=(Z_1)^N?

2. Relevant equations

3. The attempt at a solution
I'm pretty sure that this is true for a classical system, but I'm not sure if it's true for a quantum system. Does the Pauli exclusion principle spoil this somehow?

2. Apr 11, 2008

### genneth

Even without quantum considerations, you end up with over counting if the particles are identical. See Gibb's Paradox.

3. Apr 11, 2008

### Pacopag

Right. Sorry, I meant to write
$$Z={1\over {N!}}(Z_1)^N$$
Does that take care of over counting?

4. Apr 12, 2008

### genneth

It is not true for the quantum case. The quantum case is easier handled via grand-partition function.

5. Apr 12, 2008

### Pacopag

So in the quantum case, if we want to use the canonical ensemble, we have to calculate the whole partition function all in one shot?

6. Apr 13, 2008

### genneth

Yep. But like I said, usually, you calculate the grand-partition function (which factorises neatly into a function of single particle states).