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Exactly-Solvable Quantum Systems in Terms of Lambert-W Functions

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Abstract

We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schrödinger models with energy-dependent potentials, conventional Schrödinger models using the supersymmetry formalism, and two-dimensional Dirac systems. In addition, we derive Wronskian integral formulas for Lambert-W functions.

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Acknowledgements

A.M. Ishkhanyan acknowledges the support by the Russian-Armenian University and the Armenian Science Committee (SC Grants Nos. 18RF-139 and 18T-1C276).

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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

  2. Russian-Armenian University, 0051, Yerevan, Armenia

    Artur M. Ishkhanyan

  3. Institute for Physical Research, NAS of Armenia, 0203, Ashtarak, Armenia

    Artur M. Ishkhanyan

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  1. Axel Schulze-Halberg
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  2. Artur M. Ishkhanyan
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Correspondence to Axel Schulze-Halberg.

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Schulze-Halberg, A., Ishkhanyan, A.M. Exactly-Solvable Quantum Systems in Terms of Lambert-W Functions. Few-Body Syst 61, 12 (2020). https://doi.org/10.1007/s00601-020-1546-4

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