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We study a system of $A$ identical interacting bosons trapped by an externalfield by solving ab initio the many-body Schroedinger equation. A completesolution by using, for example, the traditional hyperspherical harmonics (HH)basis develops serious problems due to the large degeneracy of HH basis,symmetrization of the wave function, calculation of the matrix elements, etc.for large $A$. Instead of the HH basis, here we use the "potential harmonics"(PH) basis, which is a subset of HH basis. We assume that the contribution tothe orbital and grand orbital [in $3(A-1)$-dimensional space of the reducedmotion] quantum numbers comes only from the interacting pair. This impliesinclusion of two-body correlations only and disregard of all higher-bodycorrelations. Such an assumption is ideally suited for the Bose-Einsteincondensate (BEC), which is extremely dilute. Unlike the $(3A-4)$ hypersphericalvariables in HH basis, the PH basis involves only three {\it{active}}variables. It drastically reduces the number of coupled equations andcalculation of the potential matrix becomes tremendously simplified, as itinvolves integrals over only three variables for any $A$. One can easilyincorporate realistic atom-atom interactions in a straight forward manner. Westudy the ground and excited state properties of the condensate for bothattractive and repulsive interactions for various particle number.Comment: 36 pages, 7 included figures, plain late

Potential harmonics expansion method for trapped interacting bosons: Inclusion of two-body correlation