Quasi-exact solvability and the direct approach to invariant subspaces
We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/51461 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/51461 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Differential-operators Lame equation Potentials Algebra Física-Modelos matemáticos Física matemática |
| Sumario: | We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: we show that the generalized Lame potential possesses four algebraic sectors, and describe a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic. |
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