Ideal Quantum Gases in D-dimensional Space and Power-law Potentials

Abstract

We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. Form such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose-Einstein condensation can set up in a confining power-law potential if and only if $D/2+D/n>1$, where $D$ is the space dimension and $n$ is the power-law exponent.

18 pages, Latex, to be published in Journal of Mathematical Physics

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