  The Gross-Pitaevskii equation assumes that all (identical) bosons of a
condensate reside in a single one-particle function. Here, we raise the
question whether it always provides the best mean-field ansatz for condensates,
leading to the lowest mean-field ground state energy. To this end, we derive a
mean-field approach allowing for bosons to reside in several different
one-particle functions. The number of bosons in each of these functions is a
variational parameter minimizing the energy. The energy and one-particle
functions at these optimal numbers can be determined directly. A numerical
example is presented demonstrating that the mean-field energy of trapped bosons
can be below that provided by the Gross-Pitaevskii equation. Implications are
discussed.
