Inverse spectral problem for the Schrödinger operator on the square lattice

2023/06/23 by D yu Wu, Wu, Dongjie, Chuan‐Fu Yang +3 · 1 citation
Mathematics · #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2306.13303

openalex publication_date 2023/06/23 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28

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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