  We consider a model dissipative quantum-mechanical system realized by
coupling a quantum oscillator to a semi-infinite classical string which serves
as a means of energy transfer from the oscillator to the infinity and thus
plays the role of a dissipative element. The coupling between the two --
quantum and classical -- parts of the compound system is treated in the spirit
of the mean-field approximation and justification of the validity of such an
approach is given. The equations of motion of the classical subsystem are
solved explicitly and an effective dissipative Schrodinger equation for the
quantum subsystem is obtained. The proposed formalism is illustrated by its
application to two basic problems: the decay of the quasi-stationary state and
the calculation of the nonlinear resonance line shape.
