|
Título:
|
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
|
|
Autores:
|
Gómez-Ullate Otaiza, David ;
Grandati, Yves ;
Milson, Robert
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
IOP publishing ltd, 2014-01-10
|
|
Dimensiones:
|
application/pdf
|
|
Nota general:
|
info:eu-repo/semantics/openAccess
|
|
Idiomas:
|
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Física: Física-Modelos matemáticos
,
Materia = Ciencias: Física: Física matemática
,
Tipo = Artículo
|
|
Resumen:
|
We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux-Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2m, and they are indexed by the partitions ? of m. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2l + 3 recurrence relation where l is the length of the partition ?. Explicit expressions for such recurrence relations are given.
|
|
En línea:
|
https://eprints.ucm.es/id/eprint/30746/1/gomez-ullate04preprint.pdf
|
