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A new Darboux algorithm for mapping Schrödinger onto Klein–Gordon equations

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Abstract

We construct Darboux transformations that map one-dimensional stationary Schrödinger equations onto Klein–Gordon partner equations. This mapping does not require the stationary energy to attain a fixed value, and it keeps transformed potentials energy-independent. As a particular application of our method, we generate Klein–Gordon equations that admit solutions of bound-state type in terms of exceptional orthogonal polynomials.

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All data generated or analyzed during this study are included in this published article.

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Authors and Affiliations

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

    Axel Schulze-Halberg

  2. 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. A new Darboux algorithm for mapping Schrödinger onto Klein–Gordon equations. Eur. Phys. J. Plus 138, 1117 (2023). https://doi.org/10.1140/epjp/s13360-023-04724-5

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