On the spectral estimates for the Schr\"odinger operator on $\Z^d,\ d\ge3$

TL;DR

This paper provides precise estimates for the number of negative eigenvalues of the discrete Schrödinger operator on multidimensional integer lattices, enhancing understanding of its spectral properties.

Contribution

It introduces sharp bounds for negative eigenvalues of the discrete Schrödinger operator on or d3, advancing spectral analysis techniques.

Findings

Sharp estimates for negative eigenvalues

Improved spectral bounds for or d3

Enhanced understanding of spectral properties

Abstract

For the discrete Schr\"odinger operator we obtain sharp estimates for the number of negative eigenvalues.