Two-body interaction. II. Inverse scattering problem, phase-equivalent nonlocal potentials, relativistic generalization, and choice problems for scattering data

Abstract

In the previous paper [1], we formulated a general setting of the inverse scattering problem for the stationary Schrodinger equation on the semiaxis with nonlocal potentials υl(k, p) for a given lth partial channel. An exhaustive function-parametrized solution of the problem was presented, i.e., an explicit analytic description of the family of phase-equivalent scattering wave functions ψl(+)(k,p) in the momentum space was given. In the present paper, we discuss the following problems: (a) continuing the previous discussion in [1], we list some questions related to the choice of input scattering data, (b) study an interpretation of results obtained in [1] just in terms of nonlocal potentials, (c) treat relativization problems; (d) and investigate possible extensions of the suggested approach to some more general settings of the inverse scattering problem. Directions of further investigations are also discussed.