Exceptional orthogonal polynomials and the Darboux transformation

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 polynomi...

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Detalles Bibliográficos
Autores: Gómez-Ullate Otaiza, David, Kamran, N., Milson, R.
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/44630
Acceso en línea:https://hdl.handle.net/20.500.14352/44630
Access Level:acceso abierto
Palabra clave:51-73
Shape-invariant potentials
Quasi-exact solvability
Quantum-mechanics
Supersymmetry
Systems
Física-Modelos matemáticos
Física matemática
Descripción
Sumario: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.