Numerical calculation of the dependence of chemical potential on temperature for ideal quantum gases in 1,2 and 3-dimensional spaces

Abstract

In this study, we use the Gauss–Kronrod quadrature rule with Brent’s method to numerically calculate the chemical potentials of ideal quantum gases in 1, 2, and 3-dimensional spaces as functions of absolute temperature. Our numerical results are validated by the analytical formulae in [Cowan, B. 2019, Journal of Low Temperature Physics, 197 (5-6), 412-44]. In vice versa, we can evaluate the applicability of these proposed formulae in low- and high-temperature regimes. The results in this work are initiated for the ongoing project to analytical and numerical calculations of other thermodynamic quantities of ideal quantum gases in 1, 2, and 3-dimensional spaces such as energy, heat capacity, and entropy.