Non-relativistic bound state solutions with α-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures

E. Omugbe; O. E. Osafile; I. B. Okon; E. S. Eyube; E. P. Inyang; U. S. Okorie; A. Jahanshir; C. A. Onate

doi:10.1140/epjd/s10053-022-00395-6

2021 Impact factor 1.611

Atomic, Molecular, Optical and Plasma Physics

Eur. Phys. J. D (2022) 76: 72
https://doi.org/10.1140/epjd/s10053-022-00395-6

Regular Article – Quantum Information

Non-relativistic bound state solutions with α-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures

E. Omugbe¹^a, O. E. Osafile¹, I. B. Okon², E. S. Eyube³, E. P. Inyang⁴, U. S. Okorie⁵, A. Jahanshir⁶ and C. A. Onate⁷

¹ Department of Physics, Federal University of Petroleum Resources, 330102, Effurun, Delta State, Nigeria
² Theoretical Physics Group, Department of Physics, University of Uyo, 520101, Uyo, Nigeria
³ Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
⁴ Department of Physics, National Open University of Nigeria, Abuja, Nigeria
⁵ Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, Nigeria
⁶ Department of Physics and Engineering Sciences, Buein Zahra Technical University, 3451866391, Qazvin, Iran
⁷ Department of Physical Sciences, Landmark University, 251101, Omu-Aran, Kwara State, Nigeria

^a omugbeekwevugbe@gmail.com

Received: 24 January 2022
Accepted: 5 April 2022
Published online: 24 April 2022

Abstract

In this work, we studied the bound states and quantum theoretic-information measurements of an -deformed Kratzer-type potential with the Schrodinger equation. The ground state wave function in position-momentum spaces and the energy spectra equations for arbitrary quantum numbers are obtained in closed-form via the super-symmetric WKB method and Fourier transform. The obtained energy equation is bounded and reduces to the molecular Kratzer-type energy and the hydrogenic Coulomb’s energy upon proper adjustment of potential parameters. The wave function was used to obtain the Fisher, Shannon, Rényi and Tsallis theoretic-information measures numerically. Our results for the information measures obey the local Fisher inequality and the Bialynicki-Birula–Mycielski inequality. The Rényi and Tsallis entropies in position-momentum spaces were obtained for the index number and as a function of the potential parameter. The results of the theoretic-information quantities and probability densities revealed that the potential parameters strongly influence the localization and delocalization of the position of a nano particle.