Oscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schr?dinger’s Equation
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- 作者：Maángeles García-Ferrero ; David Gómez-Ullate
- 关键词：34C10 ; 33C45 ; 81Q80 ; Sturm–Liouville problem ; Wronskian determinant ; zeros ; oscillation ; classical orthogonal polynomials ; exceptional polynomials
- 刊名：Letters in Mathematical Physics
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：105
- 期：4
- 页码：551-573
- 全文大小：267 KB
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- 刊物主题：Physics
Mathematical and Computational Physics
Statistical Physics
Geometry
Group Theory and Generalizations - 出版者：Springer Netherlands
- ISSN：1573-0530
文摘
The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schr?dinger’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 Szeg?. 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.