Прямая и обратная задача рассеяния на всей оси для одномерного оператора Шредингера с потенциалом типа ступеньки

Abstract

The scattering problem is considered on the whole axis for a one-dimensional Schr¨odinger operator with potential which tends to different limits at ±∞. The scattering data are defined, and their properties are studied. The necessary and sufficient conditions for the reconstruction of the potential by these data are found.