Study of weakly interacting trapped Bose gas

We have obtained expressions for single particle density and two particle density of weakly interacting trapped quantum gases. These are valid for all temperature and in any dimension. These expressions have been simplified and expressed in terms of non-interacting single particle density. The ground fluctuations for T<Tc in grand canonical ensemble has been treated with care using the method of Kocharovsky et al. [Phys. Rev. A 61, 053606 (2000)]. Some numerical results are presented in one and three dimension for isotropic harmonically trapped Bose gas with contact interactions. It is seen that boson density decreases with increasing repulsive interactions. The expression for critical temperature is also shown to agree with earlier result and is in accordance with experiments.