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Analytical Solution of the Schrödinger Equation for the Linear Combination of the Manning–Rosen and the Class of Yukawa Potentials

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Russian Physics Journal Aims and scope

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning–Rosen potential plus the Yukawa class. To overcome the difficulties arising in case of l ≠ 0 in the centrifugal part of the Manning–Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. Also eigenfunctions expressed in terms of hypergeometric functions are obtained. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

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Authors and Affiliations

  1. Baku State University, Baku, Azerbaijan

    G. A. Bayramova

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  1. G. A. Bayramova
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Correspondence to G. A. Bayramova.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 157–169, September, 2021.

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Bayramova, G.A. Analytical Solution of the Schrödinger Equation for the Linear Combination of the Manning–Rosen and the Class of Yukawa Potentials. Russ Phys J 64, 1758–1773 (2022). https://doi.org/10.1007/s11182-022-02517-4

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  • DOI: https://doi.org/10.1007/s11182-022-02517-4

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