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Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential (2505.06142v1)
Published 9 May 2025 in math.AP, math-ph, and math.MP
Abstract: We consider the dynamical system with boundary control for the vector Schr\"odinger 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 Schr\"odinger equation. We then develop a strategy for solving the inverse problem for the Schr\"odinger equation using this method with other techniques of the Boundary control method.