Eur. Phys. J. D (2021) 75: 53
https://doi.org/10.1140/epjd/s10053-021-00059-x

Regular Article - Molecular Physics and Chemical Physics

Bound and scattering states solutions of the Klein–Gordon equation with generalized Mobius square potential in D-dimensions

¹ Department of Physics, Akwa Ibom State University, P M B 1167, Ikot Akpaden, Uyo, Nigeria
² Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Nigeria
³ Department of Physics, University of South Africa, 1710, Florida, Johannesburg, South Africa
⁴ Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, 123, Al-Khod, Muscat, Sultanate of Oman
⁵ Research Laboratory on Energy and Matter for Nuclear Science Development (LR16CNSTN02), National Center for Nuclear Sciences and Technologies, Sidi Thabet Technopark 2020, Tunis, Tunisia

^a uduakobongokorie@aksu.edu.ng

Received: 2 December 2020
Accepted: 23 January 2021
Published online: 10 February 2021

Abstract

In this study, the Klein–Gordon equation (KGE) was solved with the generalized Mobius square (GMS) potential using the functional analysis approach (FAA) in D-dimensions. By employing the Pekeris-type approximation scheme, the relativistic and nonrelativistic bound state energies were obtained in closed form. Also, the expression for the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of nitrogen monoiodide (NI) diatomic molecule were studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule. Hence, this concept is applicable in the areas of chemical physics, nuclear and particle physics.

Graphic abstract: In this study, the relativistic and nonrelativistic bound state energies of KGE with the GMS potential were obtained in D-dimensions using the FAA. In addition, the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of NI diatomic molecule were studied. The inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule was obtained at unique quantum states.