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Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (1996) Quasiexactly solvable potentials on the line and orthogonal polynomials. Journal of mathematical physics, 37 (8). pp. 39543972. ISSN 00222488

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Official URL: http://dx.doi.org/10.1063/1.531591
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http://scitation.aip.org  Publisher 
Abstract
In this paper we show that a quasiexactly solvable (normalizable or periodic) onedimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a threeterm recursion relation. in particular, we prove that (normalizable) exactly solvable onedimensional systems are characterized by the fact that their associated polynomials satisfy a twoterm recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary onedimensional quasiexactly 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 

Additional Information:  ©1996 American Institute of Physics. 
Subjects:  Sciences > Physics > PhysicsMathematical 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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