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American Journal of Physics

Factorization Types and SU(1, 1)

D. S. Carlstone

Published Oct 1, 1972• 2 citations
Publisher

Abstract

For a particular form of the radial Schrödinger equation it is possible to define SU(1, 1) as a noninvariance group. From the SU(1, 1) algebra and the properties of the unitary irreducible representations, one can easily find the energy eigenvalues. It is observed that the equation is essentially the standard form of the C-type factorization (in the classification of Infeld and Hull). Transformations exist which allow the B, D, and F factorization types to be solved by the same method. General expressions are found for the eigenvalues corresponding to each of the relevant factorization types and a few specific examples are given. The eigenfunctions for the C-type and F-type problems are also discussed.

DOI
10.1119/1.1986870

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