Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2015
• Main Authors: Egorova, I., Gladka, Z., Lange, T.L., Teschl, G.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/118023
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials / I. Egorova, Z. Gladka, T.L. Lange, G. Teschl // Журнал математической физики, анализа, геометрии. — 2015. — Т. 11, № 2. — С. 123-158. — Бібліогр.: 44 назв. — англ.

We study the direct and inverse scattering problem for the one-dimensional Schrödinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to its asymptotics. Our results g...