RT Journal Article
T1 Oscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schrodinger's Equation
A1 Garcia Ferrero, María Ángeles
A1 Gómez-Ullate Otaiza, David
AB 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.
PB Kluwer Academic
SN 0377-9017
YR 2015
FD 2015-04
LK https://hdl.handle.net/20.500.14352/24007
UL https://hdl.handle.net/20.500.14352/24007
LA eng
NO © 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.
NO Spanish MINECO-FEDER
DS Docta Complutense
RD 10 abr 2025