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

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Abstract

In this work, we studied the bound states and quantum theoretic-information measurements of an \(\alpha\)-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 \(q = 0.5\) and \(q = 2\) 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.

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Authors and Affiliations

  1. Department of Physics, Federal University of Petroleum Resources, Effurun, 330102, Delta State, Nigeria

    E. Omugbe & O. E. Osafile

  2. Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, 520101, Nigeria

    I. B. Okon

  3. Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria

    E. S. Eyube

  4. Department of Physics, National Open University of Nigeria, Abuja, Nigeria

    E. P. Inyang

  5. Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, Nigeria

    U. S. Okorie

  6. Department of Physics and Engineering Sciences, Buein Zahra Technical University, 3451866391, Qazvin, Iran

    A. Jahanshir

  7. Department of Physical Sciences, Landmark University, Omu-Aran, 251101, Kwara State, Nigeria

    C. A. Onate

Authors
  1. E. Omugbe
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  2. O. E. Osafile
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  3. I. B. Okon
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  4. E. S. Eyube
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  5. E. P. Inyang
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  6. U. S. Okorie
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  7. A. Jahanshir
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  8. C. A. Onate
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Contributions

EO, CAO and IBO wrote the first draft. ESE, EPI and USO carried out result confirmation and editing. AJ and OEO carried out literature search and proofreading.

Corresponding author

Correspondence to E. Omugbe.

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Data Availability Statement

The data used in this work were obtained numerically from the analytical solutions and equations within the article, therefore no data were used.

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Omugbe, E., Osafile, O.E., Okon, I.B. et al. Non-relativistic bound state solutions with α-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures. Eur. Phys. J. D 76, 72 (2022). https://doi.org/10.1140/epjd/s10053-022-00395-6

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