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.