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