  The weakly interacting trapped Bose gases have been customarily described
using the mean-field approximation in the form of the Gross-Pitaevskii
equation. The mean-field approximation, however, has certain limitations, in
particular it can not describe correlations between particles. We introduce
here an alternative variational approach, based on the correlated Gaussian
method, which in its simplest form is as fast and simple as the mean-field
approximation, but which allows successive improvements of the trial
wave-function by including correlations between particles.
