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Previously, we investigated the statistical thermodynamics of ideal gases
using a rather ad hoc combination of classical and
quantum mechanics. (See, for example, Sections 7.7 and
7.8.) In fact, we employed classical mechanics to deal with
the translational degrees of freedom of the constituent particles, and quantum
mechanics to deal with the non-translational degrees of freedom. Let us
now discuss ideal gases from a purely quantum-mechanical standpoint. It turns
out that this approach is necessary in order to treat either very low-temperature or
very high-density gases. Furthermore, it also allows us to investigate
completely non-classical
``gases,'' such as photons, or the conduction electrons in a metal.

Richard Fitzpatrick
2016-01-25