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By employing the Pekeris approximation, the D-dimensional Schrödinger 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 eigenvalues are given in a closed form, and the corresponding normalised 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 quantisation rule approach, particularly those derived by considering Woods–Saxon potential without deformation and/or without ring shape interaction.

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential