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Bose Einstein condensation of gases in a harmonic potential trap

One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose - Einstein Condensation (DEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.