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arXiv · 1804.05751

Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials

A. M. Escobar-Ruiz·J. C. López Vieyra·P. Winternitz·I. Yurdusen
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Abstract

Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordinates and admit an independent fourth-order integral of motion. The general form of the potentials satisfies a linear ODE. In the classical case, the standard potentials coincide with the Tremblay-Turbiner-Winternitz (TTW) or Post-Winternitz (PW) models. In the quantum case new superintegrable systems are obtained, in addition to the TTW and PW ones. Their classical limit is free motion.

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A. M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz, I. Yurdusen. 2018-04-16. Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials. https://doi.org/10.1088/1751-8121/aae291

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