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The mean ground state occupation number and condensate fluctuations ofinteracting and non-interacting Bose gases confined in a harmonic trap areconsidered by using a canonical ensemble approach. To obtain the mean groundstate occupation number and the condensate fluctuations, an analyticaldescription for the probability distribution function of the condensate isprovided directly starting from the analysis of the partition function of thesystem. For the ideal Bose gas, the probability distribution function is foundto be a Gaussian one for the case of the harmonic trap. For the interactingBose gas, using a unified approach the condensate fluctuations are calculatedbased on the lowest-order perturbation method and on Bogoliubov theory. It isfound that the condensate fluctuations based on the lowest-order perturbationtheory follow the law $<delta^{2}N_{\bf 0}>\sim N$, while the fluctuationsbased on Bogoliubov theory behave as $N^{4/3}$.Comment: RevTex 11 pages,5 eps figures, to appear in Phy. Rev.

Canonical statistics of trapped ideal and interacting Bose gases