An exact Feynman-type presentation of the grand canonical partition function and averages as series over cycles for a system of noninteracting identical particles with a spin in an arbitrary external field is derived, and a numerical procedure for obtaining $\mu \left(\beta \right)$ and other dependencies at constant N is developed. It is shown that the same series can be obtained also from the conventional form of the grand potential $\Omega$ (i.e., a sum over single-particle energy states). Numerical calculations at constant N are carried out for quantum gas of bosons and fermions in three-dimensional harmonic field and in the Pöschl-Teller potential.

• Received 14 July 1998

DOI:https://doi.org/10.1103/PhysRevE.59.168