  A variational basis set motivated by mean-field theory is utilized to
describe the Bose-Einstein condensate within the adiabatic hyperspherical
coordinate framework. The simplest single-orbital variant of this treatment
reproduces many of the ground state properties predicted by the
Gross-Pitaevskii equation. But a multi-orbital improvement to the basis set
yields a better representation of particle correlations and of the critical
number where the condensate collapses for a negative two-body scattering
length. The method also produces systematic deviations from Bogoliubov theory
for the fundamental monopole excitation frequency.
