Quantum mechanics for Hamiltonians defined as quadratic forms

Barry Simon9780691080901, 0691080909

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.