Remarks on the treatments of nonsolvable potentials

Abstract

A recently introduced scheme is extended to propose an algebraic nonperturbative approach for the analyticaltreatment of Schrodinger equations with nonsolvable potentials involving an exactly solvable potential form together withan additional potential term. As an illustration the procedure is successfully applied to the Cornell potential by meansof very simple algebraic manipulations. However, instead of providing numerical eigenvalues for the only consideration ofthe small strength of the related linear potential as in the previous reports, the present model puts forward a clean routeto interpret related experimental or precise numerical results involving a wide range of the linear potential strengths. Wehope this new technique will shed some light on the questions concerning the limitations of the traditional perturbationtechniques.