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

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.

Graphic Abstract

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data included in this manuscript are available on request by contacting the corresponding author.]

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Okorie, U.S., Ikot, A.N., Edet, C.O. et al. Bound and scattering states solutions of the Klein–Gordon equation with generalized Mobius square potential in D-dimensions. Eur. Phys. J. D 75, 53 (2021). https://doi.org/10.1140/epjd/s10053-021-00059-x

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Keywords

  • Bound states
  • Scattering phase shift
  • Klein–Gordon equation
  • Energy eigenvalues
  • Generalized Mobius square potential
  • Eigenfunctions