A note on eigenvalue bounds for Schr\"odinger operators

TL;DR

This paper introduces a new bound on the eigenvalues of non-self-adjoint Schrödinger operators with complex potentials, achieved through a weighted $L^2$ estimate of the Laplacian's resolvent, advancing spectral analysis techniques.

Contribution

It provides a novel eigenvalue bound for complex-valued Schrödinger operators using weighted $L^2$ resolvent estimates, extending existing spectral bounds.

Findings

New eigenvalue bounds for non-self-adjoint Schrödinger operators

Weighted $L^2$ resolvent estimates for the Laplacian

Improved understanding of spectral properties with complex potentials

Abstract

We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.