Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation

Details Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation

2010-08-12

arxiv.org/abs/1008.2035v2

Phys.Rev.Lett.105:210402,2010

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

10.1103/PhysRevLett.105.210402

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 $\hbar$ obey 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 $\hbar$ explicitly.

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