Thermodynamic properties of an ideal Fermi gas in an external potential with U=br(t) in any dimensional space

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(epsilon), 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 mu, 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. [S1050-2947(98)02508-6]