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Dirac-like Hamiltonians associated to Schrödinger factorizations

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Abstract

In this work, we have extended the factorization method of scalar shape-invariant Schrödinger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schrödinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere \({{\mathcal {S}}}^2\) and a second one, having a non-Hermitian character, from the hyperbolic space \({{\mathcal {H}}}^2\).

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Acknowledgements

This work was partially supported by Junta de Castilla y León (BU229P18) and by Ankara University BAP No. 20L0430005. D. Demir Kızılırmak acknowledges Ankara Medipol University.

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Authors and Affiliations

  1. Department of Medical Services and Techniques, Ankara Medipol University, 06050, Ankara, Turkey

    D. Demir Kızılırmak

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

    Ş. Kuru

  3. Departamento de Física Teórica, Atómica y Óptica, and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain

    J. Negro

Authors
  1. D. Demir Kızılırmak
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  2. Ş. Kuru
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  3. J. Negro
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Correspondence to Ş. Kuru.

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Kızılırmak, D.D., Kuru, Ş. & Negro, J. Dirac-like Hamiltonians associated to Schrödinger factorizations. Eur. Phys. J. Plus 136, 668 (2021). https://doi.org/10.1140/epjp/s13360-021-01642-2

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01642-2

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