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Redundant poles of the S-matrix for the one-dimensional Morse potential

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Abstract

We analyze the structure of the scattering matrix, S(k), for the one-dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of antibound poles, there exist infinite redundant poles, on the positive imaginary axis, which do not correspond to either of the other types. We explain in detail the role of these redundant poles, in particular when they coincide with the bound poles. This can be solved analytically and exactly. In addition, we obtain wave functions for all these poles and ladder operators connecting them.

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Acknowledgements

This work was partially supported by Junta de Castilla y León (BU229P18, VA137G18). Ş. Kuru acknowledges Ankara University and the warm hospitality at Department of Theoretical Physics, University of Valladolid, where this work has been done.

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Authors and Affiliations

  1. Dept. Física Teórica, Atómica y Optica and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain

    M. Gadella, A. Hernández-Ortega & J. Negro

  2. Department of Physics, Faculty of Science, Ankara University, 06100, Ankara, Turkey

    Ş. Kuru

Authors
  1. M. Gadella
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  2. A. Hernández-Ortega
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  3. Ş. Kuru
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  4. J. Negro
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Correspondence to J. Negro.

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Gadella, M., Hernández-Ortega, A., Kuru, Ş. et al. Redundant poles of the S-matrix for the one-dimensional Morse potential. Eur. Phys. J. Plus 135, 822 (2020). https://doi.org/10.1140/epjp/s13360-020-00833-7

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00833-7

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