Inverse scattering problems with the potential known on an interior subinterval

Yongxia Guo, Guangsheng Wei

Shaanxi Normal University, School of Mathematics and Information Science, Xi'an 710062, PR China

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.

Key words and phrases: Schrödinger equation, inverse scattering problem, potential recovery with partial data.

MSC: 34A55, 34L25, 34L40.

Received: 14.06.2016
Revised: 15.05.2017

Language: English

DOI: 10.15407/mag15.02.225

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