Calculation of Bose-Einstein Condensation of Gases in a Harmonic Potential Trap Using A Macro Canonical Ensemble by Use of The Mathematical and Hermitian Functions

Abstract

In this work, a mathematical analysis of Bose-Einstein condensation (BEC) for a device of particles by zero spin which has no interaction on each other in one harmonic potential trap has been discussed. It is indicated that a trapped device, quantitatively and qualitatively, differs from non-trapped device of free boson gas. One of its most important differences is that in contrast to a free boson gas device, there is no critical temperature for phase transition in a harmonic oscillator trap. In this paper, BEC in a harmonic oscillator trap in numerical and analytical points of view by using macro canonical ensemble, Mathematica software and Hermitian functions have been investigated.