Two-Body Interaction. I. Inverse Scattering Problem, Nonlocal Potentials, and a Conception of Quantum Measurement Theory

The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a nontraditional setting: the scattering wave function in the momentum representation is recovered immediately from the scattering data. The solution we find for the problem in question is given by a family of phase-equivalent wave functions with explicitly controlled functional-analytic arbitrariness. This arbitrariness corresponds to the arbitrariness in the choice of phase-equivalent nonlocal potentials and causes the necessary to include some additional concepts of quantum measurement theory to a complete description of quantum-mechanical systems. The mathematical apparatus of the approach thus developed is illustrated by the example of describing the nucleon-nucleon interaction in uncoupled partial channels.