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Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel
(1996)
*Quasi-exactly solvable potentials on the line and orthogonal polynomials.*
Journal of mathematical physics, 37
(8).
pp. 3954-3972.
ISSN 0022-2488

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Official URL: http://dx.doi.org/10.1063/1.531591

## Abstract

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. in particular, we prove that (normalizable) exactly solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the kth moment grows Like the kth power of a constant as k tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.

Item Type: | Article |
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Additional Information: | ©1996 American Institute of Physics. |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 31428 |

Deposited On: | 15 Jul 2015 15:42 |

Last Modified: | 10 Dec 2018 15:10 |

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