Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 2, pp. 225-238   https://doi.org/10.15407/mag15.02.225     ( to contents , go back )
https://doi.org/10.15407/mag15.02.225

Inverse Scattering Problems with the Potential Known on an Interior Subinterval

Yongxia Guo

Shaanxi Normal University, School of Mathematics and Information Science, Xi'an 710062, PR China
E-mail: hailang615@126.com

Guangsheng Wei

Shaanxi Normal University, School of Mathematics and Information Science, Xi'an 710062, PR China
E-mail: weimath@vip.sina.com

Received June 14, 2016, revised May 15, 2017.

Abstract

The inverse scattering problem for one-dimensional Schrödinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely determined by the mixed scattering data consisting of the scattering matrix, known potential on a finite interval, and one nodal point on the known interval for each eigenfunction.

Mathematics Subject Classification 2000: 34A55, 34L25, 34L40.
Key words: Schrödinger equation, inverse scattering problem, potential recovery with partial data.

Download 320354 byte View Contents