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Symmetry 2012, 4(3), 452-473; doi:10.3390/sym4030452

Supersymmetric Quantum Mechanics and Solvable Models

1,* , 1
1 Department of Physics, Loyola University Chicago, 1032 W. Sheridan Rd., Chicago, IL 60660, USA 2 Department of Science and Mathematics, Columbia College Chicago, 600 S. Michigan Ave., Chicago, IL 60605, USA
* Author to whom correspondence should be addressed.
Received: 29 June 2012 / Revised: 20 July 2012 / Accepted: 31 July 2012 / Published: 16 August 2012
(This article belongs to the Special Issue Supersymmetry)
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We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of ħ-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on ħ.
Keywords: supersymmetry; quantum mechanics; shape invariance supersymmetry; quantum mechanics; shape invariance
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bougie, J.; Gangopadhyaya, A.; Mallow, J.; Rasinariu, C. Supersymmetric Quantum Mechanics and Solvable Models. Symmetry 2012, 4, 452-473.

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