Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
Copyright policy )Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta. All quantum mechanical potentials that do not satisfy any linear differential equation are found. They do however satisfy nonlinear ODEs. We show that these equations always have the Painlev�� property and integrate them in terms of known Painlev�� transcendents or elliptic functions.
36 pages
- University of Queensland Australia
- University of Queensland Australia
- University of Montreal Canada
- Centre de Recherches Mathématiques
- University of Queensland Australia
Painlevé-type functions, Painlevé transcendent, Fourth order integral of motion, superintegrable system, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), 2611 Modelling and Simulation, fourth order integral of motion, Painleve transcendent, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, 3100 Physics and Astronomy, 3109 Statistical and Nonlinear Physics, 2613 Statistics and Probability, 2610 Mathematical Physics, Mathematical Physics
Painlevé-type functions, Painlevé transcendent, Fourth order integral of motion, superintegrable system, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), 2611 Modelling and Simulation, fourth order integral of motion, Painleve transcendent, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, 3100 Physics and Astronomy, 3109 Statistical and Nonlinear Physics, 2613 Statistics and Probability, 2610 Mathematical Physics, Mathematical Physics
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