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...
| Autores: | , , |
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| 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 |
| 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. |
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