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Exact solutions for bound states of nonrelativistic \({{\mathcal {PT}}}\)-symmetric potentials by using SUSYQM approach: quadratic potential and hyperbolic Schiöberg-type potential

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Abstract

In this study, the exact solutions of the bound states of the two \({{\mathcal {PT}}}\)-symmetric potentials: quadratic and hyperbolic Schiöberg-type potentials for the one-dimensional Schrödinger equation are obtained by using the SUSYQM approach. Solving the Schrödinger wave equations, the real energy eigenvalues and normalized wave functions are obtained. Some special cases of interest are discussed.

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Acknowledgements

The authors would like to thank the editor and the referees for their comments and suggestions. They also thank the Algerian government for the financial assistance allocated within the framework of PRFU Project under the code B00L02UN250120180018.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Frères Mentouri Constantine 1, Route d’Ain El-Bey, 25000, Constantine, Algeria

    N. Zaghou, F. Benamira & L. Guechi

  2. Département des Sciences de la Matière, Faculté des Sciences, Université de Médéa, Pôle Urbain, 26000, Médéa, Algeria

    N. Zaghou

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  1. N. Zaghou
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  2. F. Benamira
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  3. L. Guechi
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Correspondence to N. Zaghou.

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Zaghou, N., Benamira, F. & Guechi, L. Exact solutions for bound states of nonrelativistic \({{\mathcal {PT}}}\)-symmetric potentials by using SUSYQM approach: quadratic potential and hyperbolic Schiöberg-type potential. Indian J Phys 95, 1445–1452 (2021). https://doi.org/10.1007/s12648-020-01809-0

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  • DOI: https://doi.org/10.1007/s12648-020-01809-0

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