JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.51, no.45, 2018 (SCI-Expanded)
Article / Article
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Science Citation Index Expanded (SCI-EXPANDED), Scopus
superintegrability, separation of variables, standard potentials, higher order integrals of motion, CONFORMALLY FLAT SPACES, CLASSICAL STRUCTURE-THEORY, 3RD-ORDER INTEGRALS, STACKEL TRANSFORM, QUANTUM, SYMMETRIES, CLASSIFICATION, SEARCH, TTW
Hacettepe University Affiliated:
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space arc 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.