Inverse scattering problem for one-dimensional Schrödinger operators related to the general Stark effect
This paper discusses the inverse scattering problem for the one- dimensional Schrödinger operator on (-\(\infty,\infty)\), \(H=H_ 0+q(x)\), \(H_ 0=-d^ 2/dx^ 2+Q(x)\) with \(q\in C^{\infty}_ 0({\mathbb{R}})\), \(Q\in C^ 1({\mathbb{R}})\). It is proved that q(x) can be determined by the scattering data. The method used in this work provides a general framework which can be applied both to the Stark effect operator \((Q(x)=x)\) and to the zero potential operator \((Q(x)=0)\).
scientific article; zbMATH DE number 4146672