New superintegrable models on spaces of constant curvature
| Autor: | Joanna Gonera, Cezary Gonera |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems Pöschl–Teller potential Geodesic Integrable system 010308 nuclear & particles physics Mathematical analysis Separation of variables General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) 01 natural sciences Hamiltonian system Constant curvature 0103 physical sciences Polar coordinate system Exactly Solvable and Integrable Systems (nlin.SI) 010306 general physics Mathematical Physics Harmonic oscillator |
| DOI: | 10.48550/arxiv.1907.11578 |
| Popis: | It is known that the fairly (most?) general class of 2D superintegrable systems defined on 2D spaces of constant curvature and separating in (geodesic) polar coordinates is specified by two types of radial potentials (oscillator or (generalized) Kepler ones) and by corresponding families of angular potentials. Unlike the radial potentials the angular ones are given implicitly (up to a function) by, in general, transcendental equation. In the present paper new two-parameter families of angular potentials are constructed in terms of elementary functions. It is shown that for an appropriate choice of parameters the family corresponding to the oscillator/Kepler type radial potential reduces to Poschl-Teller potential. This allows to consider Hamiltonian systems defined by this family as a generalization of Tremblay-Turbiner-Winternitz (TTW) or Post-Winternitz (PW) models both on plane as well as on curved spaces of constant curvature. Comment: 33 pages; 3 figures |
| Databáze: | OpenAIRE |
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