Shape invariant hypergeometric type operators with application to quantum mechanics

TL;DR

This paper explores shape invariant hypergeometric operators linked to orthogonal polynomials and Schrödinger equations, extending the mathematical framework to define new operators with applications in quantum mechanics.

Contribution

It introduces an extended formalism for shape invariant operators related to hypergeometric equations and Schrödinger-type systems, broadening the scope of quantum mechanical models.

Findings

Defined new shape invariant operators related to hypergeometric functions

Connected these operators to Schrödinger equations in quantum mechanics

Extended the mathematical formalism for analyzing such operators

Abstract

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape invariant operators. All the considered shape invariant operators are directly related to Schrodinger type equations.