Cauchy problem and averaging in Fock space

We investigate a Cauchy problem in the Fock space for a system consisting o f a two-level seem, a quantum held, and a classical held. A solution estima te is obtained for the Cauchy problem with initial data from a special clas s. This class is invariant with respect to the dynamic semigroup of the sys tem. We propose an averaging method for solving the Cauchy problem in the c ase where the Hamiltonian parameters differ greatly in the order of magnitu de. An estimate of the averaging error is obtained.