Series representations for calculations in quantum statistics

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Abstract
The mathematical methods used to average a function of energy over the Maxwell–Boltzmann (MB), Bose–Einstein (BE), and Fermi–Dirac(FD) statistics are compared. Blankenbecler’s method converts the FD integrals into a series of differentiations which converge rapidly if the Fermi energy is large compared to kT. The BE integrals may be obtained from the corresponding MB integral by setting the chemical potential equal to zero and multiplying by a slowly converging numerical series. In each case a single integral of general form is used to calculate familiar quantities like chemical potential, energy, and heat capacity.

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