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Shape Invariance and Its Connection to Potential Algebra
Supersymmetry and Integrable Models
  • Asim Gangopadhyaya, Loyola University Chicago
  • Jeffrey Mallow, Loyola University Chicago
  • Uday P. Sukhatme, University of Illinois at Chicago
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Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority of these potentials have also been shown to possess a potential algebra, and hence are also solvable by group theoretical techniques. In this paper, for a subset of solvable problems, we establish a connection between the two methods and show that they are indeed equivalent.

Author Posting. © Asim Gangopadhyaya, Jeffry Mallow, Uday Sukhatme, 1998. This presentation is posted here by permission of the authors for personal use, not for redistribution. The presentation was published online on 14 May 1998.

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Creative Commons Attribution-Noncommercial-No Derivative Works 3.0
Citation Information
Gangopadhyaya, A, J Mallow, and U Sukhatme. "Shape invariance and its connection to potential algebra."