On the spectrum of discrete Schrödinger equation with one-dimensional perturbation

2016/09/18 by V. V. Borzov, Borzov, V. V., E. V. Damaskinsky +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1609.05527

openalex publication_date 2016/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the spectrum of the discrete Schrödinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of absence of singular part of the spectrum. We calculated also the eigenvalue that appears if this condition is not true. In the last part of our paper we give few remarks on the case of two-dimensional perturbations.

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