The properties of an ideal Fermi gas in an external potential in any dimensional space are studied, based on the semiclassical (Thomas-Fermi) approximation. The general analytical expressions of the total particle number $N,$ density of states $D\left(\varepsilon \right),$ Fermi energy $E_F,$ total energy $E,$ and heat capacity $C$ have been derived, where $N,$ $E,$ and $C$ are expressed by the Fermi integration. Moreover, the analytical expressions of the total energy $E,$ chemical potential μ, and heat capacity $C$ in the high- and low-temperature approximations are given. From these results, how the characteristics of the Fermi gas depend on an external potential and the dimension of space is discussed.

• Received 10 March 1998

DOI:https://doi.org/10.1103/PhysRevA.58.1445