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

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dc.contributor.authorGarcia Ferrero, María Ángeles
dc.contributor.authorGómez-Ullate Otaiza, David
dc.date.accessioned2023-06-18T06:44:49Z
dc.date.available2023-06-18T06:44:49Z
dc.date.issued2015-04
dc.description© 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.
dc.description.abstractThe 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.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipSpanish MINECO-FEDER
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/30042
dc.identifier.doi10.1007/s11005-015-0751-4
dc.identifier.issn0377-9017
dc.identifier.officialurlhttp://dx.doi.org/10.1007/s11005-015-0751-4
dc.identifier.relatedurlhttp://link.springer.com
dc.identifier.relatedurlhttp://arxiv.org/abs/1408.0883
dc.identifier.urihttps://hdl.handle.net/20.500.14352/24007
dc.issue.number4
dc.journal.titleLetters in mathematical physics
dc.language.isoeng
dc.page.final573
dc.page.initial551
dc.publisherKluwer Academic
dc.relation.projectIDMTM2012-31714
dc.relation.projectIDFIS2012-38949-C03-01
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordOrthogonal polynomials
dc.subject.keywordZeros
dc.subject.keywordFormula
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleOscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schrodinger's Equation
dc.typejournal article
dc.volume.number105
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