Shape Invariance and Its Connection to Potential Algebra

Details Shape Invariance and Its Connection to Potential Algebra Shape Invariance and Its Connection to Potential Algebra

1998-05-14

arxiv.org/abs/quant-ph/9805042v1

Physics

Quantum Physics

Latex File, 10 pages, One figure available on request. Appeared in the proceedings of the workshop on "Supersymmetric Quantum

Scientific paper

10.1007/BFb0105329

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.

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