Application of Non-Bijective Transformations to Various Potentials

TL;DR

This paper reviews non-bijective quadratic transformations generalizing classical transformations and presents new results on Lie algebras under constraints and applications to wave equations for different potentials in three and five dimensions.

Contribution

It introduces new findings on Hurwitz transformations, their Lie algebra structures, and applications to wave equations, extending classical transformation methods.

Findings

Lie algebras under constraints for Hurwitz transformations

Applications to wave equations in R^3 and R^5

Generalization of quadratic transformations

Abstract

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