The Post-Winternitz system on spherical and hyperbolic spaces: a proof of the superintegrability making use of complex functions and a curvature-dependent formalism

DOI10.1016/j.physleta.2015.07.043zbMath1374.37085OpenAlexW1105780944MaRDI QIDQ1681103

Manuel F. Rañada

Publication date: 23 November 2017

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2015.07.043

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials, Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems, Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability, Quasi-bi-Hamiltonian structures of the 2-dimensional Kepler problem, Quasi-bi-Hamiltonian structures and superintegrability: study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion, Bi-Hamiltonian structure of the bi-dimensional superintegrable nonlinear isotonic oscillator, Curvature as an Integrable Deformation, Superintegrability of three-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems, Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S ³ and on the hyperbolic space H ³

Cites Work

• Unnamed Item
• Superintegrable systems on spaces of constant curvature
• A unified approach to quantum and classical TTW systems based on factorizations
• Integrable generalizations of oscillator and Coulomb systems via action-angle variables
• On the superintegrability of TTW model
• Classical and quantum superintegrability with applications
• A new approach to the higher order superintegrability of the Tremblay–Turbiner–Winternitz system
• Infinite families of superintegrable systems separable in subgroup coordinates
• Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
• Families of superintegrable Hamiltonians constructed from exceptional polynomials
• Coupling constant metamorphosis andNth-order symmetries in classical and quantum mechanics
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• An infinite family of superintegrable deformations of the Coulomb potential
• Superintegrability and higher order integrals for quantum systems
• {\cal N}=2 supersymmetric extension of the Tremblay–Turbiner–Winternitz Hamiltonians on a plane
• An infinite family of solvable and integrable quantum systems on a plane
• Non-symplectic symmetries and bi-Hamiltonian structures of the rational harmonic oscillator
• Complete sets of invariants for dynamical systems that admit a separation of variables
• Higher order superintegrability of separable potentials with a new approach to the Post–Winternitz system
• A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities
• Families of classical subgroup separable superintegrable systems
• Superintegrability of the Tremblay–Turbiner–Winternitz quantum Hamiltonians on a plane for oddk
• The Tremblay–Turbiner–Winternitz system on spherical and hyperbolic spaces: superintegrability, curvature-dependent formalism and complex factorization
• Periodic orbits for an infinite family of classical superintegrable systems