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

Supersymmetric Quantum Mechanics and Solvable Models

1,* , 1, 1 and 2
Received: 29 June 2012; in revised form: 20 July 2012 / Accepted: 31 July 2012 / Published: 16 August 2012
(This article belongs to the Special Issue Supersymmetry)
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.
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
Download PDF Full-Text [507 KB, uploaded 16 August 2012 09:03 CEST]

Export to BibTeX |
EndNote


MDPI and ACS Style

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

AMA Style

Bougie J, Gangopadhyaya A, Mallow J, Rasinariu C. Supersymmetric Quantum Mechanics and Solvable Models. Symmetry. 2012; 4(3):452-473.

Chicago/Turabian Style

Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry; Rasinariu, Constantin. 2012. "Supersymmetric Quantum Mechanics and Solvable Models." Symmetry 4, no. 3: 452-473.

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
{"cc_re__cc_re__cc_by_3_0": ["content=\"Asim Gangopadhyaya\">\n            <meta name=\"dc.creator\" content=\"Jeffry Mallow\">\n            <meta name=\"dc.creator\" content=\"Constantin Rasinariu\">\n        \n    <meta name=\"dc.type\" content=\"Review\">\n    <meta name=\"dc.source\" content=\"Symmetry 2012, Vol. 4, Pages 452-473\">\n    <meta name=\"dc.date\" content=\"2012-08-16\">\n            <meta name =\"dc.identifier\" content=\"10.3390/sym4030452\">\n    \n    <meta name=\"dc.publisher\" content=\"Molecular Diversity Preservation International\">\n    <meta name=\"dc.rights\" content=\"http://creativecommons.org/licenses/by/3.0/\">\n    <meta name=\"dc.format\" content=\"application/pdf\" >\n    <meta name=\"dc.language\" content=\"en\" >\n\t<meta name=\"dc.description\" content=\"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", "IL 60605, USA\n\t\t    \t\t  \t\t\t\t</div>\n\n\t\t<div class=\"corspnd\">* Author to whom correspondence should be addressed. </div></div>\n\n<div class=\"art-pubhistory\">Received: 29 June 2012; in revised form: 20 July 2012 / Accepted: 31 July 2012 / Published: 16 August 2012</div>\n\n<div class=\"belongsTo\">(This article belongs to the  Special Issue <a href=\"/journal/symmetry/special_issues/supersymmetry\">Supersymmetry</a>)</div>\n<div class=\"licenseText\">\n<em>This is an open access article distributed under the <a href=\"http://creativecommons.org/licenses/by/3.0/\" target=\"_blank\">\nCreative Commons Attribution License</a> which permits unrestricted use, distribution, \nand reproduction in any medium, provided the original work is properly cited.</em>\n</div>\n\n<div id=\"pdf_loaded\" style=\"display:none\">No</div>\n\n\n<div id=\"tabs\"  style=\"padding: 1em\">\n  <ul class=\"ui-tabs-nav\">\n   \t<li><a href=\"#tabs-0\">&nbsp;Abstract&nbsp;</a></li>\n   \t   \t<li><a href=\"#tabs-5\">PDF Full-Text</a></li>\n   \t   \t\n    <li><a href=\"#tabs-1\">\n        \t\t\t\tCitations to this Article (4) \n\t\t\t    \t</a></"], "copyright__copyright__copyright": ["m Mechanics and Solvable Models. Symmetry 2012, 4, 452-473.\n\nAMA Style\n\nBougie J, Gangopadhyaya A, Mallow J, Rasinariu C. Supersymmetric Quantum Mechanics and Solvable Models. Symmetry. 2012; 4(3):452-473.\n\nChicago/Turabian Style\n\nBougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry; Rasinariu, Constantin. 2012. \"Supersymmetric Quantum Mechanics and Solvable Models.\" Symmetry 4, no. 3: 452-473.\n\nSymmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert"]}