On the Quantum Correction for Thermodynamic Equilibrium

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.