Analytical boundstate solutions of the Schrödinger equation for the ManningRosen plus Hulthén potential within SUSY quantum mechanics
Abstract
In this paper, the boundstate solution of the modified radial Schrödinger equation is obtained for the ManningRosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the NikiforovUvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 January 2018
 DOI:
 10.1142/S0217751X18500215
 Bibcode:
 2018IJMPA..3350021A
 Keywords:

 Nikiforov─Uvarov method;
 Manning─Rosen plus Hulthén potential;
 supersymmetric quantum mechanics;
 03.65.Ge;
 Solutions of wave equations: bound states