Abstract
Knowledge of the chemical potential is essential in application of the Fermi–Dirac and the Bose–Einstein distribution functions for the calculation of properties of quantum gases. We give expressions for the chemical potential of ideal Fermi and Bose gases in 1, 2 and 3 dimensions in terms of inverse polylogarithm functions. We provide Mathematica functions for these chemical potentials together with low- and high-temperature series expansions. In the 3d Bose case we give also expansions about T_{{{{mathrm {B}}}}}. The Mathematica routines for the series allow calculation to arbitrary order.
Highlights
The properties of ideal Fermi and Bose gases are the starting points for the understanding of the low-temperature behaviour of a broad range of physical systems, including electrons in metals [1,2], the helium liquids [3,4] and systems of trapped gases [5]
Fermi–Dirac and Bose–Einstein functions have been found from tables and power series expansions
The 1938 paper by McDougall and Stoner [10] gave extensive tables for fermions and there was a discussion of the corresponding functions for bosons by London [11], with series expansions given by Robinson [12] and generalized by Clunie [13]
Summary
The properties of ideal Fermi and Bose gases are the starting points for the understanding of the low-temperature behaviour of a broad range of physical systems, including electrons in metals [1,2], the helium liquids [3,4] and systems of trapped gases [5]. The properties of ideal quantum gases are expressed, conveniently and succinctly in terms of the so-called Fermi–Dirac and Bose–Einstein functions. Essential to this is knowledge of the chemical potential [9]. In this paper we provide Mathematica functions to obtain the chemical potential From these it is straightforward to evaluate properties of Bose and Fermi gases. At high temperatures the way that the Bose and Fermi gases deviate from the classical is instructive
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
