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Hartmann Potential with a Minimal Length and Generalized Recurrence Relations for Matrix Elements

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Abstract

In this work we study the Schrödinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of deformation \(\beta \) and show that some degenerate states are removed. We give analytic expressions for the solutions of the diagonal matrix elements. Finally, we derive a generalized recurrence formula for the angular average values.

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Authors and Affiliations

  1. Département de Physique, Faculté des Mathématiques et des Sciences de la Matière, Université Kasdi Merbah, Ouargla, Algeria

    Lamine Khodja

  2. Laboratoire de Physique Théorique, Faculté des Sciences Exactes, Université de Bejaia, 06000, Bejaia, Algeria

    Lamine Khodja & Mohamed Achour

  3. Département de Physique, Faculté des Sciences de la Matière, Université de Batna, 1 Hadj Lakhdar, Batna, Algeria

    Slimane Zaim

Authors
  1. Lamine Khodja
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  2. Mohamed Achour
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  3. Slimane Zaim
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Correspondence to Lamine Khodja.

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Khodja, L., Achour, M. & Zaim, S. Hartmann Potential with a Minimal Length and Generalized Recurrence Relations for Matrix Elements. Few-Body Syst 61, 17 (2020). https://doi.org/10.1007/s00601-020-01552-6

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  • DOI: https://doi.org/10.1007/s00601-020-01552-6

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