  With radiofrequency fields one can control ultracold atoms in magnetic traps.
These fields couple the atomic spin states, and are used in evaporative cooling
which can lead to Bose-Einstein condensation in the atom cloud. Also, they can
be used in controlled release of the condensate from the trap, thus providing
output couplers for atom lasers. In this paper we show that the time-dependent
multistate models for these processes have exact solutions which are
polynomials of the solutions of the corresponding two-state models. This allows
simple, in many cases analytic descriptions for the time-dependent control of
the magnetically trapped ultracold atoms.
