Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials

C.-L. Ho
2011 Progress of theoretical physics  
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
more » ... of a deformation function and its derivative.
doi:10.1143/ptp.126.185 fatcat:qf4i6jqma5gfvcw7hilpmnknei