Article,

On the Quantum Correction For Thermodynamic Equilibrium

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Physical Review, 40 (5): 749--759 (Jun 1, 1932)
DOI: 10.1103/physrev.40.749

Abstract

The probability of a configuration is given in classical theory by the Boltzmann formula exp-V/hT where V is the potential energy of this configuration. For high temperatures this of course also holds in quantum theory. For lower temperatures, however, a correction term has to be introduced, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.

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