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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