Darboux transformations for quasi-exactly solvable Hamiltonians

Details Darboux transformations for quasi-exactly solvable Hamiltonians Darboux transformations for quasi-exactly solvable Hamiltonians

2002-01-24

arxiv.org/abs/quant-ph/0201105v1

Physics

Quantum Physics

11 pages, Latex

Scientific paper

10.1142/S0217751X02009953

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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