Singularity in Potential, Perturbation and Variational Methods

TL;DR

This paper investigates the energy levels and splitting of heavy quarkonia considering singular potential terms, comparing perturbation and variational methods to address numerical solution challenges.

Contribution

It introduces a comparative analysis of perturbation and variational approaches for singular potentials in heavy quarkonia.

Findings

Perturbation and variational methods yield consistent energy eigenvalues.

Singular potential terms significantly affect quarkonium energy levels.

The study provides a framework for handling singularities in quantum systems.

Abstract

In this work, we carefully study the energy eigen-values and splitting of heavy quarkonia as there exist $1/r^3$ and $\delta^3(\vec r)$ singular terms in the potential which make a direct numerical solution of the Schr\"{o}dinger equation impossible. We compare the results obtained in terms of perturbation and variational methods with various treatments.