Fourth-order superintegrable systems separating in polar coordinates. II. Standard potentials Article Swipe

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A. M. Escobar-Ruiz , J. C. López Vieyra , P. Winternitz , İsmet Yurduşen ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1088/1751-8121/aae291 · OA: W4232598985

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.