Inverse spectral problem for the Schrödinger operator on the square lattice

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-25 DOI:10.1088/1361-6420/ad3332

Dongjie Wu, Chuan-Fu Yang, Natalia Pavlovna Bondarenko

引用次数: 0

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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方格上薛定谔算子的逆谱问题

我们考虑了与方阵相关的量子图上的反谱问题。假设边上的势是紧凑支撑和对称的，我们证明了图的有限部分上边界值问题的 Dirichlet 到 Neumann 映射唯一地决定了势。我们获得了一种基于将微分薛定谔算子还原为离散算子的重构程序。作为主要结果的一个推论，我们证明了连续谱中任何给定开集的所有能量的 S 矩阵唯一地指定了方格上的势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.