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?