  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.
