## partition function

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?
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 Even without quantum considerations, you end up with over counting if the particles are identical. See Gibb's Paradox.
 Right. Sorry, I meant to write $$Z={1\over {N!}}(Z_1)^N$$ Does that take care of over counting? What about the quantum case?

## partition function

It is not true for the quantum case. The quantum case is easier handled via grand-partition function.
 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?
 Yep. But like I said, usually, you calculate the grand-partition function (which factorises neatly into a function of single particle states).

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