Application of Non-Bijective Transformations to Various Potentials

Abstract

Some results about non-bijective quadratic transformations generalizing the Kustaanheimo-Stiefel and the Levi-Civita transformations are reviewed in §1. The three remaining sections are devoted to new results: §2 deals with the Lie algebras under constraints associated to some Hurwitz transformations; §3 and §4 are concerned with several applications of some Hurwitz transformations to wave equations for various potentials in $R^3$ and $R^5$.