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Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials

By C. -L. Ho

Abstract

We show how all the quantal systems related to the exceptional Laguerre and Jacobi polynomials can be constructed in a direct and systematic way, without the need of shape invariance and Darboux-Crum transformation. Furthermore, the prepotential need not be assumed a priori. The prepotential, the deforming function, the potential, the eigenfunctions and eigenvalues are all derived within the same framework. The exceptional polynomials are expressible as a bilinear combination of a deformation function and its derivative.Comment: PTPTex, 18 pages, no figures. Presentation improved (especially Sect. 2 and 4.4), references updated, typos corrected (especially range of integration in Eq. (4.12)). To appear in Prog. Theor. Phy

Topics: Mathematical Physics, Mathematics - Spectral Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Quantum Physics
Year: 2011
DOI identifier: 10.1143/PTP.126.185
OAI identifier: oai:arXiv.org:1104.3511
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