On the Quantum Correction for Thermodynamic Equilibrium

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Abstract
The behavior of any system at high enough temperatures approaches that of its classical counterpart. The probability of any configurational position is then proportional to exp—U/kT, with U the potential energy. Wigner has shown that quantum‐mechanical deviations, as the temperature is lowered, may be approximated by multiplication of this with 1–f, where f is a function proportional to h2 and having terms in T−2 and terms in T−3. This type of approximation is unsatisfactory for a system of many degrees of freedom, that is, one of many dependent molecules. For such a system it is shown that instead of Wigner's approximation we may replace the classical potential U in the exponent by U—kTf, where f is the same as Wigner's function.

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