Exact solutions of the pseudo-Coulomb potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method

TL;DR

This paper derives exact bound-state solutions for the D-dimensional Schrödinger equation with a pseudo-Coulomb plus ring-shaped potential using the Nikiforov-Uvarov method, providing explicit wave functions and energy levels.

Contribution

It presents a novel analytical solution for a combined potential in D-dimensions, including explicit wave functions and energy spectra using the Nikiforov-Uvarov method.

Findings

Exact energy eigenvalues derived for the potential

Wave functions expressed in terms of orthogonal polynomials

General results reduce to known special cases

Abstract

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for an alternative (often used) pseudo-Coulomb potential-plus- ring-shaped potential of the form $V(r)=-% \frac{a}{r}+\frac{b}{r^{2}}+\frac{\beta \cos ^{2}\theta}{r^{2}\sin ^{2}\theta }+c$ by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the radial and angular parts of the wave functions in terms of orthogonal polynomials. The total energy of the system is different from the pseudo-Coulomb potential because of the contribution of the angular part. The general results obtained in this work can be reduced to the standard forms given in literature.