Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces

  title={Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces},
  author={{\'A}ngel Ballesteros and Francisco J. Herranz},
  journal={Journal of Physics A: Mathematical and Theoretical},
The superposition of the Kepler–Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper, we present the generalization of this result to the N-dimensional spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry approach that makes use of the curvature… 

A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system

The N-dimensional quantum Hamiltonian is shown to be exactly solvable for any real positive value of the parameter η. Algebraically, this Hamiltonian system can be regarded as a new maximally

Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St

The Stackel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler{Coloumb potentials, in order to obtain ma- ximally superintegrable classical

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by where q i and p i are generic canonical variables, γ n are arbitrary coefficients, and N ∈ N . For N = 2,

Variables separation and superintegrability of the nine-dimensional MICZ-Kepler problem

The nine-dimensional MICZ-Kepler problem is of recent interest. This is a system describing a charged particle moving in the Coulomb field plus the field of a SO(8) monopole in a nine-dimensional

Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems

The classical Kepler{Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is

Superintegrable systems, polynomial algebra structures and exact derivations of spectra

Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract

The anisotropic oscillator on the 2D sphere and the hyperbolic plane

An integrable generalization on the 2D sphere S2 and the hyperbolic plane H2 of the Euclidean anisotropic oscillator Hamiltonian with ‘centrifugal’ terms given by is presented. The resulting

Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension

We introduce a new superintegrable Kepler–Coulomb system with non-central terms in N-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in

Classical and quantum superintegrability with applications

A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum

Classical and quantum higher order superintegrable systems from coalgebra symmetry

The N-dimensional generalization of Bertrand spaces as families of maximally superintegrable (M.S.) systems on spaces with a nonconstant curvature is analyzed. Considering the classification of



Superintegrability on N-dimensional spaces of constant curvature from so(N + 1) and its contractions

The Lie—Poisson algebra so(N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and

Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N − 3) functionally

Maximal superintegrability on N-dimensional curved spaces

A unified algebraic construction of the classical Smorodinsky–Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N + 1), ISO(N) and SO(N, 1) is presented.

Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2

The existence of superintegrable systems with n=2 degrees of freedom possessing three independent globally defined constants of motion which are quadratic in the velocities is studied on the

Dynamical symmetries in a spherical geometry. I

The two potentials for which a particle moving non-relativistically in a spherical space under the action of conservative central force executes closed orbits are found. When the curvature is zero

Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2

The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane. First, the theory of central potentials on spaces of

Completeness of multiseparable superintegrability on the complex 2-sphere

The possibility that Schrodinger's equation with a given potential can separate in more than one coordinate system is intimately connected with the notion of superintegrability. Here we demonstrate,

A new superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in three degrees of freedom, obtained as a reduction of pure Keplerian motion in six dimensions. The new Hamiltonian is a generalization of the Keplerian

On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space

We give a graphical prescription for obtaining and characterizing all separable coordinates for which the Schr?dinger equation admits separable solutions for one of the superintegrable potentials