Coulomb-oscillator duality in spaces of constant curvature

DOI10.1063/1.533263zbMath0987.81024arXivquant-ph/9906055OpenAlexW2131483544MaRDI QIDQ2737958

Ernest G. Kalnins, Willard jun. Miller, George S. Pogosyan

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9906055

zbMATH Keywords

Kepler-Coulomb problemHurwitz regularizing transformationsKustaanheimo-Stiefel regularizing transformationLevi-Civita regularizing transformations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Hamilton-Jacobi equations in mechanics (70H20)

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Cites Work

• The quantized \(\text{SU}(2)\) Kepler problem and its symmetry group for negative energies
• QUANTUM OSCILLATOR AND A BOUND SYSTEM OF TWO DYONS
• Path integral treatment of the hydrogen atom in a curved space of constant curvature. II. Hyperbolic space
• Stäckel-Equivalent Integrable Hamiltonian Systems
• An algebraic and geometric approach to non-bijective quadratic transformations
• Dynamical symmetries in a spherical geometry. I
• Dynamical symmetries in a spherical geometry. II
• Quantization of the conformal Kepler problem and its application to the hydrogen atom
• Superintegrability on the two-dimensional hyperboloid
• Contractions of Lie algebras and separation of variables
• 8D oscillator and 5D Kepler problem: The case of nontrivial constraints
• Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

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