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Oscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schrodinger's Equation

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Garcia Ferrero, María Ángeles and Gómez-Ullate Otaiza, David (2015) Oscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schrodinger's Equation. Letters in mathematical physics, 105 (4). pp. 551-573. ISSN 0377-9017

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Official URL: http://dx.doi.org/10.1007/s11005-015-0751-4




Abstract

The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schrodinger's equation to have constant sign in its domain of definition. We extend this result by giving explicit formulas for the number of real zeros of the Wronskian of an arbitrary sequence of eigenfunctions. Our results apply in particular to Wronskians of classical orthogonal polynomials, thus generalizing classical results by Karlin and SzegA. Our formulas hold under very mild conditions that are believed to hold for generic values of the parameters. In the Hermite case, our results allow to prove some conjectures recently formulated by Felder et al.


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© 2015 Springer-Verlag. The authors would like to thank Robert Milson and Antonio Durán for stimulating discussions. The elegant proof of Lemma 3.1 that uses the irreducibility of Hermite polynomials is in fact entirely due to Robert Milson. MAGF would like to thank the Department of Theoretical Physics II at Universidad Complutense for providing her with office space and all facilities. The research of DGU has been supported in part by the Spanish MINECO-FEDER Grants MTM2012 31714 and FIS2012-38949- C03-01.

Uncontrolled Keywords:Orthogonal polynomials; Zeros; Formula
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30042
Deposited On:12 May 2015 09:03
Last Modified:10 Dec 2018 15:09

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