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Higher-order Darboux transformations for the Dirac equation with position-dependent mass at nonvanishing energy

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Abstract

We construct Darboux transformations of arbitrary order for the two-dimensional Dirac equation within a position-dependent mass scenario. While we restrict the potential and the mass to a single dimension, the stationary energy remains arbitrary. We use our Darboux transformation to generate several new exactly solvable Dirac systems that admit bound states at nonzero energies.

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Authors and Affiliations

  1. Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, IN, 46408, USA

    Axel Schulze-Halberg

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  1. Axel Schulze-Halberg
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Correspondence to Axel Schulze-Halberg.

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Schulze-Halberg, A. Higher-order Darboux transformations for the Dirac equation with position-dependent mass at nonvanishing energy. Eur. Phys. J. Plus 135, 863 (2020). https://doi.org/10.1140/epjp/s13360-020-00882-y

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00882-y

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