On the number of eigenvalues of Schr\"odinger operators with complex potentials

TL;DR

This paper investigates the eigenvalues of Schrödinger operators with complex potentials in odd-dimensional spaces, providing bounds on their total number when the potential decays exponentially at infinity.

Contribution

It offers new bounds on the total number of eigenvalues for Schrödinger operators with exponentially decaying complex potentials in odd dimensions.

Findings

Bounds on the total number of eigenvalues derived

Results applicable to potentials with exponential decay

Enhanced understanding of spectral properties in complex settings

Abstract

We study the eigenvalues of Schr\"odinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where $V$ decays exponentially at infinity.