Scattering theory for three particles with pair potentials periodic in time

Scattering theory for three particles with pair potentials, periodic in time, is considered. Scattering for pair problems is preliminary studied. Finiteness of the number of quasienergetic states is proved, that in the conventional theory of scattering corresponds to the finiteness of the number of bound states. To determine wave operator the model Hilbert space and model ''undisturbed'' operator in it are built up. The boundary conditions applied on the corresponding two-particle hamiltonians, is formulated in terms of integral equation