Absence of eigenvalues of non-selfadjoint Schr\"odinger operators on the boundary of their numerical range

TL;DR

This paper establishes conditions under which non-selfadjoint Schrödinger operators lack eigenvalues on the boundary of their numerical range, extending understanding of their spectral properties.

Contribution

It introduces simple criteria based on Hildebrandt's classical result for the absence of eigenvalues on the boundary of the numerical range of such operators.

Findings

Eigenvalues are absent on the boundary under specified conditions.

Results apply to both discrete and continuous Schrödinger operators.

Provides a unified approach using classical spectral theory.

Abstract

We use a classical result of Hildebrandt to establish simple conditions for the absence of eigenvalues of non-selfadjoint discrete and continuous Schr\"odinger operators on the boundary of their numerical range.