Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials

[[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.[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子版[[countrycodes]]JP