  We use the mean-field approximation to simplify the master equation for
sympathetic cooling of Bosons. For the mean single-particle occupation numbers,
this approach yields the same equations as the factorization assumption
introduced in an erlier paper. The stationary or equilibrium solution of the
resulting master equation for the one-body density matrix shows that the
mean-field approximation breaks down whenever the fraction of condensate Bosons
exceeds ten percent or so of the total. Using group-theoretical methods, we
also solve the time-dependent master equation for the one-body density matrix.
Given the time dependence of the mean single-particle occupation numbers, this
solution is obtained by quadratures. It tends asymptotically towards the
equilibrium solution.
