Abstract
We investigate the possible factorizations of the confluent hypergeometric equation and show that this leads to a formal equivalence of the usual hydrogen atom problem with that of a set of multidimensional harmonic oscillators of appropriate classical frequency in a space of varying (even) dimensionality ranging from 4l + 4 to 2. We next use this method to investigate the solutions of some relativistic bound-state equations. As specific examples we consider Goldstein's eigenvalue problem and the Wick-Cutkosky scalar meson equation. A formal similarity also exists between the Goldstein problem and the scalar meson equation in the zero binding limit. The factorization of either of these equations leads to an infinite ladder of nonsquare integrable solutions. On the other hand, for arbitrary nonvanishing binding energies a complete solution of the scalar meson problem has been obtained by investigating the zero-energy factorization of the equation.
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