By using the mechanical exitations (excitons and phonons) of a molecular crystal the nonlinear HAMILTONian for the quantum theoretic treatment of stimulated STOKES scattering (polariton scattering) is calculated. For this purpose a special kind of adiabatic approximation described in an earlier work is used. In the HEISENBERG picture the equations of motion for photons, phonons, and excitons are derived. The field equations used in the classical theory for description of stimulated STOKES generation are deduced semi-classically by elimination of the exciton operators in the equations of motion. At last the general microscopic structure of the nonlinear coupling constants used in the classical theory is given.