A procedure for high-accuracy numerical derivation of the thermodynamic properties of ideal Bose gases

The thermodynamic functions of ideal Bose gases are important in fundamental physics and have been widely studied via both analytical and numerical methods. Studying these functions is important for undergraduates as it is the first step for exploring ultracold physics and quantum phenomena. However, the accuracy of the calculations is usually limited owing to the discontinuity of the functions at critical points. In this study, we present an analytical procedure for deriving the chemical potential, the total energy, and the heat capacity as functions of the absolute temperature. The approximated analytical results are compared with values obtained using the numerical method to evaluate their accuracy and to determine the applicable range of the procedure. Moreover, a correction for the chemical potential calculated around the critical temperature was proposed to reduce the deviation between the approximated and numerical approaches.