Determination of the self-adjoint matrix Schrödinger operators without the bound state data. (26th April 2018)

• Record Type: Journal Article
• Authors: Xu, Xiao-Chuan; Yang, Chuan-Fu
• Is Part Of: Inverse problems. Volume 34:Number 6(2018:Jun.)
• Publication Date: 2018-04-26
• Subjects: matrix Schrödinger operator -- inverse scattering problem -- exponentially decreasing potential -- mixed data; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aab929
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: (i) For the matrix Schrödinger operator on the half line, it is shown that the scattering data, which consists of the scattering matrix and the bound state data, uniquely determines the potential and the boundary condition. It is also shown that only the scattering matrix uniquely determines the self-adjoint potential and the boundary condition if either the potential exponentially decreases fast enough or the potential is known a priori on ( ), where a is an any fixed positive number. (ii) For the matrix Schrödinger operator on the full line, it is shown that the left (or right) reflection coefficient uniquely determine the self-adjoint potential if either the potential exponentially decreases fast enough or the potential is known a priori on (or ( )), where b is an any fixed number.