Perturbation of eigenvalues of the Klein Gordon operators II

TL;DR

This paper provides improved estimates for how the eigenvalues of the Klein-Gordon operator change when the potential varies, validated through exactly solvable models like Coulomb and oscillator potentials.

Contribution

It introduces refined bounds for eigenvalue perturbations of the Klein-Gordon operator and applies these to specific solvable models.

Findings

Improved eigenvalue change estimates under potential variations

Validation on Coulomb and Klein-Gordon oscillator models

Enhanced understanding of spectral stability in relativistic quantum systems

Abstract

We give estimates for the changes of the eigenvalues of the Klein Gordon operator under the change of the potential. In some relevant situations we improve the existing estimates. We test our results on some exactly solvable models (Coulomb potential, Klein-Gordon oscillator).