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Darboux transformations for quasi-exactly solvable Hamiltonians

N. Debergh·Boris F. Samsonov·B. Van Den Bossche
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Abstract

We construct new quasi-exactly solvable one-dimensional potentials through Darboux transformations. Three directions are investigated: Reducible and two types of irreducible second-order transformations. The irreducible transformations of the first type give singular intermediate potentials and the ones of the second type give complex-valued intermediate potentials while final potentials are meaningful in all cases. These developments are illustrated on the so-called radial sextic oscillator.

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N. Debergh, Boris F. Samsonov, B. Van Den Bossche. 2002-01-24. Darboux transformations for quasi-exactly solvable Hamiltonians. https://doi.org/10.1142/s0217751x02009953

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