Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials. (16th July 2018)

• Record Type: Journal Article
• Authors: Gómez-Ullate, David; Grandati, Yves; Milson, Robert
• Is Part Of: Journal of physics. Volume 51:Number 34(2018)
• Publication Date: 2018-07-16
• Subjects: Wronskian determinants -- exceptional orthogonal polynomials -- shape invariant potentials -- Darboux transformations -- Maya diagrams -- Durfee symbols; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aace4b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi polynomials. The equivalence formulas are richer in this case since rational Darboux transformations can be defined for four families of seed functions, as opposed to only two families in the Hermite case. The pseudo-Wronskian determinants of Laguerre and Jacobi type will thus depend on two Maya diagrams, while Hermite pseudo-Wronskians depend on just one Maya diagram. We show that these equivalence relations can be interpreted as the general transcription of shape invariance and specific discrete symmetries acting on the parameters of the isotonic oscillator and Darboux–Pöschl–Teller potential.