# Partition function problems

1. Aug 2, 2011

### Lh0907

1. The problem statement, all variables and given/known data

1. If the system, which has N identical particles, only has two possible energy states

E=0,e(e is an energy) ,what's the ensemble average of E?

2. Find the partition function which has two identical Fermion system if the energy states only have

E=0,e.

2. Relevant equations

I think what's different about partition function for identical Boson, Fermion and Boltmann stat particle?

3. The attempt at a solution

I made a solution but I'm not sure this is wrong or correct.

1. Z1 = 1 +exp(-e/kT)

Then, the total partition function is Z = (Z1)^N / (N!).

So Ensemble average of energy is <E> = (1/Z) * e * exp(-e/kt).

This is my solution.

Is this right or not?

2. Z1 = 1+exp(-e/kT)

Because of identical these Fermion -> Z = 1/2 * Z1^2

.....But it should be changed due to property of Fermion.

The first identical particle can occupy E=0,e , so Z1 = 1+exp(-e/kT).

Then, if first particle occupy state which state energy is 0, Z2 can only exp(-e/kT).

Therefore partition function is (1+exp(-e/kT))*(-e/kT).

And another sitution is first particle occupy energy e state.

Then, another partition function is (1+exp(-e/kT)*1.

I thought this is connected by linearly

Final partition function is Z = 1/2 * (1/2*((1+exp(-e/kT))*(-e/kT)+ (1+exp(-e/kT)*1))

But I believe something is wrong this second problem.

What's the wrong?