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arXiv · 2306.13303

Inverse spectral problem for the Schrödinger operator on the square lattice

Dongjie Wu·Chuan-Fu Yang·Natalia Pavlovna Bondarenko
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Abstract

We consider an inverse spectral problem on a quantum graph associated with the square lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the Dirichlet-to-Neumann map for a boundary value problem on a finite part of the graph uniquely determines the potentials. We obtain a reconstruction procedure, which is based on the reduction of the differential Schrödinger operator to a discrete one. As a corollary of the main results, it is proved that the S-matrix for all energies in any given open set in the continuous spectrum uniquely specifies the potentials on the square lattice.

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Dongjie Wu, Chuan-Fu Yang, Natalia Pavlovna Bondarenko. 2023-06-23. Inverse spectral problem for the Schrödinger operator on the square lattice. https://arxiv.org/abs/2306.13303

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