Hypergeometric type operators and their supersymmetric partners

TL;DR

This paper extends Mielnik's factorization method to hypergeometric type operators, enabling the generation of new exactly solvable quantum potentials using Riccati equations and orthogonal polynomials.

Contribution

It introduces a novel application of Mielnik's method to hypergeometric operators, providing a unified framework for solvable quantum systems with special functions.

Findings

Derived new exactly solvable potentials using hypergeometric operators.

Established a unitary framework for quantum systems solvable via orthogonal polynomials.

Connected Riccati equations with supersymmetric quantum mechanics.

Abstract

The generalization of the factorization method performed by Mielnik [J. Math. Phys. {\bf 25}, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to hypergeometric type operators. It is based on some solvable Riccati equations and leads to a unitary description of the quantum systems exactly solvable in terms of orthogonal polynomials or associated special functions.