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Applying quantum supersymmetry and perturbation theory to the energy-dependent Hulthén potential

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Abstract.

We deal with the energy-dependent Hulthén potential, by using the supersymmetric quantum mechanics and the first-order perturbation theory. We consider the Hulthén potential linearly dependent on the energy which is introduced in the coupling constant. We evaluate the energy eigenvalues and the corresponding reduced radial eigenfunctions. We compare the analytical results with the numerical solutions of the Schrödinger equation in the energy-dependent and the energy-independent cases. We then investigate the screening effect in order to determine the critical screening parameter values for each state. After that, we look into the absorption oscillator strengths for different transitions.

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Authors and Affiliations

  1. Département de Physique Théorique, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumedienne, BP 32 El-Alia, 16111, Alger, Algeria

    Elhadj Hocine & Rabia Yekken

  2. Groupe de Physique Théorique, Institut de Physique Nucléaire, IN2P3 - CNRS, Université Paris-Sud 11, 91406, Orsay Cedex, France

    Roland Lombard

Authors
  1. Elhadj Hocine
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  2. Rabia Yekken
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  3. Roland Lombard
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Correspondence to Elhadj Hocine.

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Hocine, E., Yekken, R. & Lombard, R. Applying quantum supersymmetry and perturbation theory to the energy-dependent Hulthén potential. Eur. Phys. J. Plus 134, 561 (2019). https://doi.org/10.1140/epjp/i2019-12921-6

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