Exceptional Polynomials and SUSY Quantum Mechanics

Abstract

We show that the existence of exceptional polynomials leads to the presence of non-trivial supersymmetry. The existence of these polynomials reveals several distinct isospectral potentials for the Schrödinger equation. All Schrödinger equations having Laguerre and Jacobi polynomials as their solutions, have non-trivial supersymmetric partners with corresponding exceptional polynomials as solutions.

9 pages

References in corpus (3)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• An Extension of Bochner's Problem: Exceptional Invariant Subspaces
• Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

Cited by in corpus (1)

• QHJ route to multi-indexed exceptional Laguerre polynomials and corresponding rational potentials