The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 5 1 2019 11 26 Bose Einstein condensation of gases in a harmonic potential trap Bose Einstein condensation of gases in a harmonic potential trap 11 16 613 FA M. E. Zomorrodian R. Sabili Journal Article 2019 11 26 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 (BEC). 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. 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 (BEC). 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. https://ijpr.iut.ac.ir/article_613_f29c21d4897f78948b91f03172341b7b.pdf