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

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.

arXiv comment30 pages

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• Doubly Exotic $N$th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates
• Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
• Polynomially Superintegrable Hamiltonians Separating in Cartesian Coordinates