Remarks on the treatments of nonsolvable potentials


Abstract: A recently introduced scheme is extended to propose an algebraic nonperturbative approach for the analytical treatment of Schrödinger equations with nonsolvable potentials involving an exactly solvable potential form together with an additional potential term. 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 a wide range of the linear potential strengths. We hope this new technique will shed some light on the questions concerning the limitations of the traditional perturbation techniques.

Keywords: Nonsolvable potentials, Cornell potential, perturbation theory

Full Text: PDF