Thermodynamic properties of an ideal system trapped in a generic cylindrical power-law potential

The thermodynamic properties of ideal Bose and Fermi systems trapped in an n-dimensional generic cylindrical power-law potential are studied by using the semiclassical (Thomas–Fermi) approximation. A unified description for the two quantum gases is given. Moreover, the concepts of general thermal wavelength and pseudovolume are introduced. The results obtained here are very general and significant. From them, not only the results in the relevant current literature but also some new important general conclusions, such as the general conditions and bounds for Bose–Einstein condensation, the relation between the critical temperature and the Fermi temperature, the characteristics of the heat capacity, and the significance of the general thermal wavelength, can be deduced directly.