Shape Invariance and Its Connection to Potential Algebra
Quantum Physics
2009-10-31 v1
Abstract
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.
Cite
@article{arxiv.quant-ph/9805042,
title = {Shape Invariance and Its Connection to Potential Algebra},
author = {Asim Gangopadhyaya and Jeffry V. Mallow and Uday P. Sukhatme},
journal= {arXiv preprint arXiv:quant-ph/9805042},
year = {2009}
}
Comments
Latex File, 10 pages, One figure available on request. Appeared in the proceedings of the workshop on "Supersymmetric Quantum Mechanics and Integrable Models" held at University of Illinois, June 12-14, 1997; Ed. H. Aratyn et al