  We introduce a family of correlated trial wave functions for the $N$-particle
ground state of an interacting Bose gas in a harmonic trap. For large $N$, the
correlations lead to a relative energy decrease of a fraction $3/5N$, compared
to mean field Gross-Pitaevskii theory. The kinetic energy in the weakly
confining direction turns out to be most sensitive to our correlations and,
remarkably, is higher by as much as a few per cent for condensates with atom
numbers of a few thousand. Thus, the predicted deviations from Gross-Pitaevskii
theory originating from ground state correlations might be observed in momentum
distribution measurements of small condensates.
