On eigenvalues of discrete Schr\"odinger operators with potentials of Coulomb type decay

TL;DR

This paper investigates how the eigenvalues of one-dimensional discrete Schrödinger operators are distributed within the essential spectrum when the potentials decay at a Coulomb-like rate.

Contribution

It provides new insights into the spectral properties of discrete Schrödinger operators with Coulomb-type decaying potentials, focusing on eigenvalue distribution.

Findings

Eigenvalue distribution inside the essential spectrum characterized.

Decay rate influences spectral properties significantly.

Results extend understanding of Coulomb-type potential effects.

Abstract

We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.