Density of states and thermodynamic properties of an ideal system trapped in any dimension

The density of states and thermodynamic properties of an ideal gas system t rapped in a generic power-law potential in an n-dimensional space are studi ed. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the resu lts in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Ei sntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.