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Exact solution of Schrödinger equation in (anti-)de Sitter spaces for hydrogen atom

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Abstract

We write Schrödinger equation for the Coulomb potential in both de Sitter and anti-de Sitter spaces using the Extended Uncertainty Principle formulation. We use the Nikiforov–Uvarov method to solve the equations. The energy eigenvalues for both systems are given in their exact forms, and the corresponding radial wave functions are expressed in associated Jacobi polynomials for de Sitter space, while those of anti-de Sitter space are given in terms of Romanovski polynomials. We have also studied the effect of the spatial deformation parameter on the bound states in the two cases.

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Acknowledgements

The authors would like to thank the referee for the remarks made; these have greatly improved the manuscript and thus contribute to a better understanding of the work.

Funding

Funding was provided by Direction Générale de la Recherche Scientifique et du Développement Technologique (Grant No. B00L02UN070120190003).

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Authors and Affiliations

  1. Laboratory of Photonic Physics and Nano-Materials (LPPNNM), Department of Matter Sciences, University of Biskra, Biskra, Algeria

    Mokhtar Falek & Mustafa Moumni

  2. Laboratory of Energy Engineering and Materials (LGEM), Department of Mechanics, University of Biskra, Biskra, Algeria

    Noureddine Belghar

Authors
  1. Mokhtar Falek
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  2. Noureddine Belghar
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  3. Mustafa Moumni
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Correspondence to Mustafa Moumni.

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Falek, M., Belghar, N. & Moumni, M. Exact solution of Schrödinger equation in (anti-)de Sitter spaces for hydrogen atom. Eur. Phys. J. Plus 135, 335 (2020). https://doi.org/10.1140/epjp/s13360-020-00337-4

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00337-4

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