Coulomb-oscillator duality in spaces of constant curvature

1999/06/16 by E. G. Kalnins, Willard Miller, W. Miller, Jr. +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical mechanics #Constant (computer programming) #Constant curvature #Coulomb #Curvature #Duality (order theory) #Euclidean geometry #Geometry #Kepler problem #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #SPHERES #quant-ph

paper · pdf · doi:10.1063/1.533263

published as J.Math.Phys.41:2629-2657,2000 · 33 pages, LaTeX file

arxiv created 1999/06/16 · openalex publication_date 2000/05/01 · arxiv updated 2012/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we construct generalizations to spheres of the well-known Levi-Civita, Kustaanheimo–Steifel, and Hurwitz regularizing transformations in Euclidean spaces of dimensions two, three, and five. The corresponding classical and quantum mechanical analogs of the Kepler–Coulomb problem on these spheres are discussed.

Citations

• On Hurwitz Transformations
• Deformed oscillator algebras for two-dimensional quantum superintegrable systems
• Quantum Theory of Angular Momentum

Cited by

• Position-dependent mass, finite-gap systems, and supersymmetry
• A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog