Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials
Mathematical Physics
2011-09-03 v4 math.MP
Spectral Theory
Exactly Solvable and Integrable Systems
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1104.3511,
title = {Prepotential approach to solvable rational potentials and exceptional orthogonal polynomials},
author = {C. -L. Ho},
journal= {arXiv preprint arXiv:1104.3511},
year = {2011}
}
Comments
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. Phys