Definition and existence of multichannel scattering states

The field theoretical formulation of quantum mechanics is used to consider the nonrelativistic multichannel scattering theory. With the help of appropriately constructed time dependent creation operators, Hilbert vectors are formed whose limits in time can be defined as multichannel scattering states in the usual sense. The existence of these states is proved under certain assumptions for the potential, by showing the convergence of the above mentioned operators. The commutation relations for the limits of these operators are given.