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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; in revised form: 20 July 2012 / Accepted: 31 July 2012 / Published: 16 August 2012
Abstract: 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
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MDPI and ACS Style
Bougie, J.; Gangopadhyaya, A.; Mallow, J.; Rasinariu, C. Supersymmetric Quantum Mechanics and Solvable Models. Symmetry 2012, 4, 452-473.
Bougie J, Gangopadhyaya A, Mallow J, Rasinariu C. Supersymmetric Quantum Mechanics and Solvable Models. Symmetry. 2012; 4(3):452-473.
Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry; Rasinariu, Constantin. 2012. "Supersymmetric Quantum Mechanics and Solvable Models." Symmetry 4, no. 3: 452-473.