Abstract
We systematically describe and classify one-dimensional Schrödinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe two new classes of exactly solvable Schrödinger equations that can be reduced to the Hermite equation.
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The research of J. D. was supported in part by the grant N N201 270135 of the Polish Ministry of Science and Higher Education.
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Communicated by Claude-Alain Pillet.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Dereziński, J., Wrochna, M. Exactly Solvable Schrödinger Operators. Ann. Henri Poincaré 12, 397–418 (2011). https://doi.org/10.1007/s00023-011-0077-4
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DOI: https://doi.org/10.1007/s00023-011-0077-4