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arXiv · 2505.06142

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

Sergei Avdonin·Alexander Mikhaylov·Victor Mikhaylov·Jeff Park
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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.

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Sergei Avdonin, Alexander Mikhaylov, Victor Mikhaylov, Jeff Park. 2025-05-09. Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential. https://doi.org/10.1088/1361-6420%2Fabd7cb

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