Average occupancy in systems


I wanna ask a quick question about the occupancy of energy levels in systems governed by different distributions.

There exists a system of two particles, each of which may occupy one of two energy levels. Consider three cases:
1. Distinguishable, classical particles
2. Fermions
3. Bosons

For each case, write down how many different ways there are for the particles to
occupy (i) the same state and (ii) different states.

Well, to begin with,

the fermions and bosons are indistinguishable, right?


1. i) 2 ii) 2
2. i) 2 ii) 1
3. i) 2 ii) 1



Fermions and bosons are indistinguishable, but no two fermion may occupy the same state. However, since the problem mentions "energy levels," one can assume that spin is not included in what is called a "state" in the problem. Hence, the answer given above is correct.

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