Remarks on the treatments of non-solvable potentials

TL;DR

This paper extends an algebraic non-perturbative method to analytically treat Schrödinger equations with complex potentials, exemplified by the Cornell potential, offering a new approach beyond traditional perturbation techniques.

Contribution

The paper introduces an algebraic scheme for non-solvable potentials, enabling analytical solutions and interpretation of experimental data without relying solely on numerical eigenvalues.

Findings

Successfully applied to the Cornell potential

Provides a clear interpretation of experimental results

Offers a non-perturbative alternative to traditional methods

Abstract

The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together with an additional piece. As an illustration the procedure is successfully applied to the Cornell potential by means of very simple algebraic manipulations. However, instead of providing numerical eigenvalues for the only consideration of the small strength of the related linear potential as in the previous reports, the present model puts forward a clean route to interpret related experimental or precise numerical results involving wide range of the linear potential strengths. We hope this new technique will shed some light on the questions concerning with the limitations of the traditional perturbation techniques.