Physical Review Letters
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.
Bougie, Jonathan, Asim Gangopadhyaya, and Jeffry V. Mallow. “Generation of a Complete Set of Additive Shape-Invariant Potentials from an Euler Equation.” Physical Review Letters 105, no. 21 (November 19, 2010): 210402. doi:10.1103/PhysRevLett.105.210402.
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© 2010 The American Physical Society
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.