Bound and scattering states solutions of the Klein–Gordon equation with the attractive radial potential in higher dimensions

Abstract

In this study, the Klein–Gordon equation (KGE) is solved with the attractive radial potential using the Nikiforov–Uvarov-functional-analysis (NUFA) method in higher dimensions. By employing the Greene–Aldrich approximation scheme, the approximate bound state energy equations as well as the corresponding radial wave function are obtained in closed form. Also, the expression for the scattering phase shift is obtained in D-dimensions. The effects of the screening parameter and the total angular momentum quantum number on the bound state energy and the scattering states’ phase shift are also studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift. Hence, this concept is applicable in the areas of nuclear and particle physics.