Exceptional orthogonal polynomials and the Darboux transformation
By D. Gómez‐Ullate, Niky Kamran, Robert Milson. 2010
154 citations recorded by the source corpus.
We adapt the notion of the Darboux transformation to the context of polynomial Sturm–Liouville problems. As an application, we characterize the recently described Xm 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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/19348aaee63a9ff9a1a2687cbc59cc8479fca0bd
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations (2010, unknown): “A recent report by Gomez-Ullate eta al [18] has small overlap with the present work.”
- Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials (2014, methodology): “Exceptional orthogonal polynomials have been applied to shape-invariant potentials,[12] supersymmetric transformations [5] and to discrete quantum mechanics.”