Partition Functions for Partly Classical Systems

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Abstract
A method is described for calculating the partition function of systems whose Hamiltonian operator separates into three terms of the following types. The first and second terms are functions of different sets of coordinates while the third is a small coupling term. The energy levels of the first term by itself are widely spaced compared to kT while those of the second are closely spaced. In the result given, the partition function becomes a sum over the widely spaced levels and a phase integral for the contribution of the other levels, as in the case with no coupling term, but here the effect of the coupling term is included in the integral. As an illustration it is shown that the coupling of rotational and vibrational angular momentum in a polyatomic molecule has no appreciable effect on the thermodynamic properties even though it has a marked effect on the energy levels.