title: Generation of a complete set of additive shape-invariant potentials from an Euler equation.
abstract: In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ℏ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ℏ explicitly.
authors.affiliation: Loyola University Chicago, Department of Physics, Chicago, Illinois 60660, USA. jbougie@luc.edu
authors.forename: Jonathan
authors.initials: J
authors.lastname: Bougie
authors.forename: Asim
authors.initials: A
authors.lastname: Gangopadhyaya
authors.forename: Jeffry V
authors.initials: JV
authors.lastname: Mallow