  The resources required to solve the general interacting quantum N-body
problem scale exponentially with N, making the solution of this problem very
difficult when N is large. In a previous series of papers we develop an
approach for a fully-interacting wave function with a general two-body
interaction which tames the N-scaling by developing a perturbation series that
is order-by-order invariant under a point group isomorphic with S_N . Group
theory and graphical techniques are then used to solve for the wave function
exactly and analytically at each order. Recently this formalism has been used
to obtain the first-order, fully-interacting wave function for a system of
harmonically-confined bosons interacting harmonically. In this paper, we report
the first application of this N-body wave function to a system of N
fully-interacting bosons in three dimensions. We determine the density profile
for a confined system of harmonically-interacting bosons. Choosing this simple
interaction is not necessary or even advantageous for our method, however this
choice allows a direct comparison of our exact results through first order with
exact results obtained in an independent solution. Our density profile through
first-order in three dimensions is indistinguishable from the first-order exact
result obtained independently and shows strong convergence to the exact result
to all orders.
