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Wronskian representation for confluent supersymmetric transformation chains of arbitrary order

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Abstract.

We prove that iterations of confluent supersymmetric transformations (confluent SUSY chains) in quantum mechanics can be represented through Wronskian determinants. It is further shown that the latter Wronskian representation remains valid, if the SUSY chain is built from arbitrary combinations of confluent and non-confluent subchains. In addition, we obtain an integral representation of generalized eigenfunctions for quantum-mechanical Hamiltonians that proves useful for the application of confluent SUSY chains. Our results generalize former findings for second- and third-order chains.

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Authors and Affiliations

  1. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, 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. Wronskian representation for confluent supersymmetric transformation chains of arbitrary order. Eur. Phys. J. Plus 128, 68 (2013). https://doi.org/10.1140/epjp/i2013-13068-2

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  • DOI: https://doi.org/10.1140/epjp/i2013-13068-2

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