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arXiv · 1104.3511

Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials

C. -L. Ho
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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.

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C. -L. Ho. 2011-08-06. Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials. https://doi.org/10.1143/ptp.126.185

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