The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
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Publication:3544665
DOI10.1063/1.2840463zbMath1153.81332arXiv0709.2572OpenAlexW2107812073WikidataQ115333533 ScholiaQ115333533MaRDI QIDQ3544665
José F. Cariñena, Mariano Santander, Manuel F. Rañada
Publication date: 8 December 2008
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0709.2572
Two-body problems (70F05) Applications of global differential geometry to the sciences (53C80) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)
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Cites Work
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- The path integral for the Kepler problem on the pseudosphere
- Complex Euclidean super-integrable potentials, potentials of Drach, and potential of Holt
- On some properties of harmonic oscillator on spaces of constant curvature.
- From oscillator(s) and Kepler(s) potentials to general superintegrable systems in spaces of constant curvature
- Completeness of superintegrability in two-dimensional constant-curvature spaces
- Dynamical symmetries, bi-Hamiltonian structures, and superintegrable n=2 systems
- Coulomb-oscillator duality in spaces of constant curvature
- Exact solvability of superintegrable systems
- Confocal Conics in Space-Time
- Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
- Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory
- Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform
- Geodesics and Killing tensors in mechanics
- Path integral treatment of the hydrogen atom in a curved space of constant curvature. II. Hyperbolic space
- Path integral treatment of the hydrogen atom in a curved space of constant curvature
- Dynamical symmetries in a spherical geometry. I
- Dynamical symmetries in a spherical geometry. II
- Casimir invariants for the complete family of quasisimple orthogonal algebras
- Dynamical symmetries, non-Cartan symmetries and superintegrability of then-dimensional harmonic oscillator
- Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries
- Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach
- Superintegrability on the two-dimensional hyperboloid
- The general solution of the real graded contractions of
- Maximal superintegrability onN-dimensional curved spaces
- Conformal symmetries of spacetimes
- Conformal compactification of spacetimes
- Trigonometry of complex Hermitian -type homogeneous symmetric spaces
- Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
- Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
- On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2
- On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2. II.
- An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics
- Geometry of spaces with the Jacobi metric
- Separable Potentials and a Triality in Two-Dimensional Spaces of Constant Curvature
- Three-Dimensional Isotropic Harmonic Oscillator and SU3
- Intrinsic Characterizations of Orthogonal Separability for Natural Hamiltonians with Scalar Potentials on Pseudo-Riemannian Spaces
- Superintegrability on curved spaces, orbits and momentum hodographs: revisiting a classical result by Hamilton
- On the Problem of Degeneracy in Quantum Mechanics
- Bertrand systems on spaces of constant sectional curvature. The action-angle analysis
