https://doi.org/10.1140/epjp/s13360-023-04724-5
Regular Article
A new Darboux algorithm for mapping Schrödinger onto Klein–Gordon equations
1
Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA
2
Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA
Received:
16
September
2023
Accepted:
20
November
2023
Published online:
16
December
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
