Superintegrability and Coulomb-Oscillator Duality
Levon G. Mardoyan
TL;DR
This paper reviews the Coulomb-oscillator duality in quantum mechanics, focusing on non-bijective quadratic transformations like Levi-Civita, KS, and Hurwitz transformations, highlighting their roles in connecting these fundamental systems.
Contribution
It provides a comprehensive review of the mathematical transformations underpinning Coulomb-oscillator duality in quantum mechanics.
Findings
Explains the role of Levi-Civita, KS, and Hurwitz transformations.
Highlights the non-bijective nature of these quadratic transformations.
Connects Coulomb and oscillator systems through these transformations.
Abstract
This review is devoted to the problem of Coulomb (dyon)-oscillator duality in non-relativistic quantum mechanics, which is based on the so-called non-bijective quadratic transformations, i.e. Levi-Civita transformation, Kustaanheimo--Stiefel (KS-transformation) and Hurwitz transformation.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Particle accelerators and beam dynamics · Advanced Frequency and Time Standards