# Two distinguishable particles in a box.

Hi,

I would like to determine the number of energy states two free, distinguishable particles in a box of length L have. I would then like to determine the number of states two free, indistinguishable particles, with spin 3/2 each, have in that box at the elementary level. Finally, determine the number of states in case these two particles with spin 3/2 each are distinguishable.

**1. The problem statement, all variables and given/known data**I would like to determine the number of energy states two free, distinguishable particles in a box of length L have. I would then like to determine the number of states two free, indistinguishable particles, with spin 3/2 each, have in that box at the elementary level. Finally, determine the number of states in case these two particles with spin 3/2 each are distinguishable.

**2. Relevant equations**

**3. The attempt at a solution**

I am familiar with the following formula for the energy states

E_{n}=(hbar)^{2}π^{2}n^{2}/(2mL^{2})

but am not sure how to proceed. If the particles are distinguishable, does that entail that one is a fermion whereas the other is a boson? I am not sure.

Furthermore, if the two particles have spin 3/2 each, that means they are both fermions, right? If that is correct, then, due to Pauli’s exclusion principle, the two could not be at the same state. I also know that for spin 3/2 there could be 4 particles per energy level. But again I am not sure how to coherently process the given data and would appreciate some guidance.

http://ift.tt/1bRnOPU

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