DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

In this paper, we provide a comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of the Fermi-Dirac integral function both analytically and numerically. The analytical formulae describing the dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriate approximations. Afterwards, the results are compared with the well-converged numerical calculations in order to evaluate the applicability of these formulae.