The one-dimensional inverse scattering problem for an increasing potential

In English The one-dimensional inverse scattering problem is considered for potentials that grow without limit for large values of x. The Marchenko method is established for this class of potentials, and several properties of the solution to the Schrödinger equation are developed. In the derivation of the Marchenko equation an extension of the triangularity condition is used. Some brief remarks on the relation to the inverse radial problem and the generalization to hard core potentials are made.