Some spectral bounds for Schroedinger operators with Hardy-type potentials

TL;DR

This paper derives bounds on the negative eigenvalues of Schrödinger operators with Hardy-type potentials using coordinate transformations, aiding spectral analysis in supersymmetric quantum mechanics.

Contribution

It introduces a simple coordinate transformation method to establish spectral bounds for Schrödinger operators with Hardy-type potentials, which is a novel approach.

Findings

Bounds for the number of negative eigenvalues derived

Method applicable to supersymmetric quantum models

Potentially useful for spectral analysis

Abstract

This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain supersymmetric quantum mechanical models.