广义外势中费米气体的相对论热力学性质

采用Thomas-Fermi的半经典近似方法，得到处于任意维空间一般幂函数型势阱中相对论理想费米气体的巨配分函数和巨热力学势。又用热力学基本公式得到了总粒子数、总能及热容量的解析表达式（这些表达式中都含有修正的贝赛尔函数），并在极高低温情况下得到总能量、化学势和热容的表达式。由这些结果，得到了各种因素对费米气体的影响。

Thermodynamic Properties of A Relativistic Fermi Gas Trapped in a General External Potential

Based on the semiclassical （Thomas-Fermi） approximation, the macrocanonical partition function and macrocanonical potential of a relativistic Fermi gas in a general external potential in any dimensional space are studied. The general analytical expressions of the total particle number N, total energy U and heat capacity C have been derived with thermodynamic fundamental equations, where N,U and C are expressed by the modified Bessel function. Moreover,the analytical expressions of the total energy, chemical potential and heat capacity in the high- and low-temperature approxima- tions are given. From these results, how the characteristics of the Fermi gas depend on various factors is discussed.