Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials

Details Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials

2011-04-18

arxiv.org/abs/1104.3511v4

Prog. Theor. Phys. 126 (2011), 185-201

Physics

Mathematical Physics

PTPTex, 18 pages, no figures. Presentation improved (especially Sect. 2 and 4.4), references updated, typos corrected (especia

Scientific paper

10.1143/PTP.126.185

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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