Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability

DOI10.1063/1.4975339zbMath1406.70026arXiv1701.05783OpenAlexW2581171295MaRDI QIDQ2968436

Manuel F. Rañada, José F. Cariñena, Francisco J. Herranz

Publication date: 13 March 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.05783

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Equations of motion in general relativity and gravitational theory (83C10) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (9)

Cylindrical type integrable classical systems in a magnetic field ⋮ PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian ⋮ Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials ⋮ Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials ⋮ Eisenhart lift for Euler's problem of two fixed centers ⋮ Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” ⋮ Fourth-order superintegrable systems separating in polar coordinates. II. Standard potentials ⋮ 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
• Unnamed Item
• Unnamed Item
• Nonlinear dynamics of classical counterpart of the generalized quantum nonlinear oscillator driven by position dependent mass
• An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
• Superintegrable systems on spaces of constant curvature
• A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum
• First integrals of extended Hamiltonians in \(n+1\) dimensions generated by powers of an operator
• Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform
• Two-dimensional superintegrable metrics with one linear and one cubic integral
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Classical and quantum position-dependent mass harmonic oscillators
• Exact solutions of the Schrödinger equation with position-dependent mass for some Hermitian and non-Hermitian potentials
• The Kepler problem and the Laplace-Runge-Lenz vector on spaces of constant curvature and arbitrary signature
• Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
• Dynamical trajectories of simple mechanical systems as geodesics in space with an extra dimension
• Complex Euclidean super-integrable potentials, potentials of Drach, and potential of Holt
• The Post-Winternitz system on spherical and hyperbolic spaces: a proof of the superintegrability making use of complex functions and a curvature-dependent formalism
• The Eisenhart geometry as an alternative description of dynamics in terms of geodesics
• First-order intertwining operators and position-dependent mass Schrödinger equations in \(d\) dimensions
• Effective mass Schrödinger equation and nonlinear algebras
• A maximally superintegrable system on an \(n\)-dimensional space of nonconstant curvature
• Ricci-flat spacetimes admitting higher rank Killing tensors
• The Drach superintegrable systems
• Completeness of superintegrability in two-dimensional constant-curvature spaces
• Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds
• Classical and quantum superintegrability with applications
• Higher-order superintegrability of a Holt related potential
• Yet another position-dependent mass quantum model
• Laplace–Runge–Lenz vector with spin in any dimension
• Conformal Killing vector fields and a virial theorem
• Conformal killing tensors and covariant Hamiltonian dynamics
• Extensions of Hamiltonian systems dependent on a rational parameter
• A quantum quasi-harmonic nonlinear oscillator with an isotonic term
• A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
• Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
• Geodesics and Killing tensors in mechanics
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• A generalisation of the Runge-Lenz constant of classical motion in a central potential
• Superintegrable systems with third-order integrals of motion
• Bertrand spacetimes as Kepler/oscillator potentials
• Superintegrability and higher order polynomial algebras
• Third-order superintegrable systems separating in polar coordinates
• Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry
• HIGHER ORDER FIRST INTEGRALS OF MOTION IN A GAUGE COVARIANT HAMILTONIAN FRAMEWORK
• Position-dependent mass oscillators and coherent states
• Killing tensors in spaces of constant curvature
• SYMPLECTIC STRUCTURE ON THE SET OF GEODESICS OF A RIEMANNIAN MANIFOLD
• Group theory of the Smorodinsky–Winternitz system
• Bertrand spacetimes
• Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Generalisations of the LaplaceRungeLenz Vector
• Maximal superintegrability onN-dimensional curved spaces
• Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
• The Kepler problem in Dirac theory for a particle with position-dependent mass
• Superintegrability in three-dimensional Euclidean space
• Superintegrability in a two-dimensional space of nonconstant curvature
• Hamiltonians separable in Cartesian coordinates and third-order integrals of motion
• Two kinds of generalized Taub-NUT metrics and the symmetry of associated dynamical systems
• The anisotropic oscillator on the 2D sphere and the hyperbolic plane
• Superposition of super-integrable pseudo-Euclidean potentials in N = 2 with a fundamental constant of motion of arbitrary order in the momenta
• Time-dependent Schrödinger equations with effective mass in (2 + 1) dimensions: intertwining relations and Darboux operators
• Superintegrable deformations of superintegrable systems: Quadratic superintegrability and higher-order superintegrability
• Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
• Laplace–Runge–Lenz symmetry in general rotationally symmetric systems
• Position-dependent mass Lagrangians: nonlocal transformations, Euler–Lagrange invariance and exact solvability
• Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime
• The quantum effective mass Hamilton–Jacobi problem
• Three-Dimensional Isotropic Harmonic Oscillator and SU3
• Killing tensors, warped products and the orthogonal separation of the Hamilton-Jacobi equation
• Generalised Eisenhart lift of the Toda chain
• The Tremblay–Turbiner–Winternitz system on spherical and hyperbolic spaces: superintegrability, curvature-dependent formalism and complex factorization
• Spectrum generating algebras for position-dependent mass oscillator Schrödinger equations
• Superintegrability on curved spaces, orbits and momentum hodographs: revisiting a classical result by Hamilton
• Generalized nonlinear oscillators with quasi-harmonic behaviour: Classical solutions

This page was built for publication: Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability