Document Type

Article

Publication Date

11-10-2010

Publication Title

Physical Review Letters

Volume

105

Issue

210402

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.

Identifier

10.1103/PhysRevLett.105.210402

Comments

Author Posting. © 2010 The American Physical Society. This article is posted here by permission of the American Physical Society for personal use, not for redistribution. The article published in Physical Review Letters, 105, 210402, 2010. http://dx.doi.org/10.1103/PhysRevLett.105.210402.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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