Exceptional Polynomials and SUSY Quantum Mechanics

TL;DR

This paper explores how exceptional polynomials induce non-trivial supersymmetry in quantum mechanics, revealing new isospectral potentials and extending the class of solvable Schrödinger equations with exceptional polynomial solutions.

Contribution

It demonstrates that exceptional polynomials lead to non-trivial supersymmetry and identifies new isospectral potentials in quantum mechanics.

Findings

Existence of non-trivial supersymmetry linked to exceptional polynomials

Identification of distinct isospectral potentials for Schrödinger equations

Extension of solutions to include exceptional Laguerre and Jacobi polynomials

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 Schr\"odinger equation. All Schr\"odinger equations having Laguerre and Jacobi polynomials as their solutions, have non-trivial supersymmetric partners with corresponding exceptional polynomials as solutions.