Next Article in Journal / Special Issue
Supersymmetric Sigma Model Geometry
Previous Article in Journal / Special Issue
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
Article Menu

Export Article

Open AccessReview
Symmetry 2012, 4(3), 452-473;

Supersymmetric Quantum Mechanics and Solvable Models

Department of Physics, Loyola University Chicago, 1032 W. Sheridan Rd., Chicago, IL 60660, USA
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)
View Full-Text   |   Download PDF [507 KB, uploaded 16 August 2012]   |  


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. View Full-Text
Keywords: supersymmetry; quantum mechanics; shape invariance supersymmetry; quantum mechanics; shape invariance

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top