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Identifying relationships in supersymmetric quantum mechanics

A new paper titled "Inter-relations between additive shape invariant superpotentials" by LUC Physics faculty members Jeffry Mallow, Asim Gangopadhyaya, Jonathan Bougie, and Constantin Rasinariu, and was published in Physical Letters A in February 2020. The professors' research is in supersymmetric quantum mechanics (SUSYQM). Supersymmetry assigns to each elementary particle, boson or fermion, a supersymmetric partner particle which is fermion or boson. While supersymmetric particles are yet to be found in nature, the ideas of supersymmetry has a powerful impact on ordinary quantum mechanics. First employed as a so-called “toy model” of field theory, SUSYQM was developed using the notion of “partner potentials” derivable from an underlying “superpotential.” SUSYQM was soon found to have value in its own right, with applications to resolving numerous questions in quantum mechanics and the posing of various interesting new ones. This paper examines the connections between different types of superpotentials as shown in the above figure. The authors reveal that an important class of superpotentials, known as additive shape-invariant superpotentials, can be related to each other through a series of discrete transformations. Previously, only connections among type I or among type II superpotentials were known. This paper uncovers a way to connect type I to type II superpotentials, thus providing a unitary point of view of their interconnections.