  We compare the equilibrium solution for the condensate obtained in the
mean--field approximation to the master equation for sympathetic cooling with
the one obtained by Scully for a system in contact with a heat bath with the
help of an analogy with the laser. While the mean--field approach yields
analytical formulas for the approach towards equilibrium and for the
equilibrium solution, it neglects the correlations between occupation numbers
of different single--particle states which are approximately kept in Scully's
approach. Such neglect is admissible as long as the fraction of Bosons in the
condensate does not exceed a few percent or so.
