Physics and Astronomy Publications

Document Type

Article

Publication Date

10-8-2009

Journal

Journal of Mathematical Physics

Volume

50

Issue

10

First Page

102103-1

Last Page

102103-11

URL with Digital Object Identifier

http://dx.doi.org/10.1063/1.3230482

Abstract

We present some applications of the Lambert W function (W function) to the formalism of quantum statistics (QS). We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then present some applications of this formula including Bose–Einstein systems in d dimensions, Maxwell–Boltzmann systems, and black body radiation. We also show that for the appropriate parameter values, this formula reduces to an analytic expression in connection with Wien’s displacement law that was found in a previous study. In addition, we show that for Maxwell–Boltzmann and Bose–Einstein systems, the W function allows us to express the temperature of the system as a function of the thermodynamically relevant chemical potential, the particle density, and other parameters. Finally, we explore an indirect relationship of the W function to the polylogarithm function and to the Lambert transform.

Notes

Copyright (2009) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
This article appeared in (S. R. Valluri et al., J. Math. Phys. 50, 102103 (2009)) and may be found at S. R. Valluri et al., J. Math. Phys. 50, 102103 (2009).


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