3 Quantum gases

We now move on to study quantum gases. As before, we are going to spend a

lot of time evaluating the partition function for different systems. Recall that

the partition function is defined as a sum over all eigenstates. In the world of

classical gases, we had the benefit of working over a continuous phase space,

and thus we can replace the sum by integrals. In the quantum world, this is no

longer the case, However, most of the time, the states are very closely packed,

and we might as well approximate the sum by an integral. Of course, we cannot

replace the sum just by

R

d

E

. We have to make sure we preserve the “density”