A Venn diagram for supersymmetric, exactly solvable, shape invariant, and Infeld-Hull factorizable potentials

TL;DR

This paper clarifies the relationships among supersymmetry, shape invariance, exact solvability, and factorization in quantum potentials, providing a visual Venn diagram to resolve common confusions and misconceptions.

Contribution

It defines key concepts and systematically illustrates their interrelations with a Venn diagram, clarifying the scope and connections of these topics in quantum mechanics.

Findings

Clarification of the relations among supersymmetry, shape invariance, and exact solubility.

Identification of common confusions and misconceptions in the literature.

Provision of a visual Venn diagram illustrating these relationships.

Abstract

Supersymmetry, shape invariance, exact solubility, and the factorization method are often studied together in the literature. At the dawn of these topics confusion was present in regards to their scope of applicability and the relation among them. Considerable work have been put to study and resolve the relation among two or more of these topics. These works are scattered over the literature. While looking at the literature, one can not overlook the number of places where authors confuse these terms, and concluding implications depending on wrong assumptions of the relation between two or more of these topics. In this letter we define supersymmetry, and shape invariance, and show the relations which connects them to exact solubility and the factorization method, referring to the literature for the respective detailed work and proofs. At last we conclude our letter with a Venn diagram which illustrates those relations.