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Garcia Ferrero, María Ángeles and GómezUllate 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. 551573. ISSN 03779017

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Official URL: http://dx.doi.org/10.1007/s1100501507514
URL  URL Type 

http://link.springer.com  Publisher 
http://arxiv.org/abs/1408.0883  Organisation 
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.
Item Type:  Article 

Additional Information:  © 2015 SpringerVerlag. 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 MINECOFEDER Grants MTM2012 31714 and FIS201238949 C0301. 
Uncontrolled Keywords:  Orthogonal polynomials; Zeros; Formula 
Subjects:  Sciences > Physics > PhysicsMathematical 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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