Abstract
We derive the conditions which give a well-defined meaning to the mathematical expressions appearing in the current formal scattering theory. These conditions remove some restrictions that are usually imposed on the spectra of H and H0. By these conditions we can systematically discuss many problems, such as the equivalence between two kinds of S-matrices given by Heisenberg and Dyson respectively, or as the adiabatic theorem in the quantum field theory. The rearrangement collisions can be investigated from this view-point.

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