On the inverse scattering problem for the one-dimensional Schrödinger equation with growing potential

Abstract

We consider a one-dimensional Schrödinger equation on the entire axis whose potential rapidly decreases at the left end and infinitely increases at the right end. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable. The basic Marchenko-type integral equations are investigated and their unique solvability is established.