Juriev D.V. Quantum dynamics of transition processes in the interacting systems (7K, TeX) ABSTRACT. The dynamical inverse problem of representation theory (the Wigner problem) is solved for a certain class of interactions of Hamiltonian systems. The constructed quantum dynamics describes transition processes and stationary regimes on an equal footing. Among other numerous applications the results may be useful for the description of the simultaneous quantum dynamics of the open and closed string fields in the unified string field theory with their noncanonical coupling.