Closed analytical solutions of the d-dimensional Schr\"odinger equation with deformed Woods-Saxon potential plus double ring-shaped potential

TL;DR

This paper derives closed-form solutions for the Schrödinger equation in D dimensions with a deformed Woods-Saxon plus double ring-shaped potential using AIM, extending previous methods and results.

Contribution

It provides analytical energy eigenvalues and eigenfunctions for a complex potential, generalizing prior results obtained by other methods.

Findings

Closed-form energy eigenvalues derived

Eigenfunctions expressed in hypergeometric functions

Results encompass previous models as special cases

Abstract

By employing the Pekeris approximation, the D-dimensional Schr\"odinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The energy eingenvalues are given in a closed form and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov-Uvarov method (NU) and the Improved Quantization Rule approach, particulary those derived by considering Woods-Saxon potential without deformation and/or without ring shape interaction.