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

Jonathan Bougie; Asim Gangopadhyaya; Jeffrey Mallow

doi:10.1103/PhysRevLett.105.210402

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

Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow

Department of Physics

Loyola University Chicago

Research output: Contribution to journal › Article › peer-review

Abstract

<p> 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 &hstrok; 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 &hstrok; explicitly.</p>

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	105
Issue number	210402
DOIs	https://doi.org/10.1103/PhysRevLett.105.210402
State	Published - Nov 10 2010

Keywords

supersymetric quantum mechanics

Disciplines

Physics

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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 &hstrok; 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 &hstrok; explicitly.",

keywords = "supersymetric quantum mechanics",

author = "Jonathan Bougie and Asim Gangopadhyaya and Jeffrey Mallow",

note = "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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PY - 2010/11/10

Y1 - 2010/11/10

N2 - 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 &hstrok; 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 &hstrok; explicitly.

AB - 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 &hstrok; 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 &hstrok; explicitly.

KW - supersymetric quantum mechanics

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DO - 10.1103/PhysRevLett.105.210402

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VL - 105

JO - Physics: Faculty Publications and Other Works

JF - Physics: Faculty Publications and Other Works

IS - 210402

ER -

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

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