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The sum of states of an assembly in statistical equilibrium may be transformed into an integral in phase space, which is analogous to the classical Gibbs phase integral. With the use of an equation obtained by Bloch it is possible to expand the quantum phase integral in powers of Planck's constant h. The present method of treating the problem supplements that of Wigner and of Uhlenbeck and Gropper by furnishing a more convenient means of obtaining the h-expansion.
John G. Kirkwood (1933) studied this question.