It is our purpose in this monograph to present a complete, rigorous
mathematical treatment of two body quantum mechanics for a wider class
of potentials than is normally treated in the literature. At the same time,
we will review the theory of the "usual" Kato classes, although no attempt has been made to make this review exhaustive or complete. The
scope of what we present is best delineated by stating the limits of this
work: we take for granted the standard Hilbert space formalism, and our
main goal is to prove forward dispersion relations from first principles. For example we do not assume the Lippman-Schwinger equation but prove it within the framework of time-dependent scattering theory.