Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential

Abstract

We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the dynamical Dirichlet--to--Neumann operator. We first provide a method to recover spectral data for an abstract system from dynamic data and apply it to the Schrödinger equation. We then develop a strategy for solving the inverse problem for the Schrödinger equation using this method with other techniques of the Boundary control method.

References in corpus (2)

• Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials
• Relationship between different types of inverse data for the one-dimensional Schrödinger operator on a half-line

Cited by in corpus (1)

• Discrete dynamical systems: inverse problems and related topics