Exceptional orthogonal polynomials and the Darboux transformation



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Gómez-Ullate Otaiza, David and Kamran, N. and Milson, R. (2010) Exceptional orthogonal polynomials and the Darboux transformation. Journal of physics A: Mathematical and theoretical, 43 (43). ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8113/43/43/434016


We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described X(m) Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.

Item Type:Article
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© IOP Publishing Ltd.
The research of DGU was supported in part by MICINN-FEDER grant MTM2009- 06973 and CUR-DIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 105490-2004. The research of RM was supported in part by NSERC grant RGPIN-228057-2004.

Uncontrolled Keywords:Shape-invariant potentials; Quasi-exact solvability; Quantum-mechanics; Supersymmetry; Systems
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30805
Deposited On:12 Jun 2015 08:51
Last Modified:10 Dec 2018 15:09

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