# Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability

@article{Ballesteros2011QuantumMO, title={Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability}, author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni}, journal={arXiv: Quantum Physics}, year={2011} }

## 54 Citations

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

- Physics
- 2013

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…

Classical and quantum higher order superintegrable systems from coalgebra symmetry

- Mathematics, Physics
- 2013

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…

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

- Physics
- 2011

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…

Classical and quantum superintegrability with applications

- Mathematics
- 2013

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…

Exactly solvable deformations of the oscillator and Coulomb systems and their generalization

- Mathematics
- 2014

We present two maximally superintegrable Hamiltonian systems Hλ and Hη that are defined, respectively, on an N-dimensional spherically symmetric generalization of the Darboux surface of type III and…

Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion

- Mathematics
- 2017

It is natural to investigate if the quantization of integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of…

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

- Mathematics
- 2017

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian H = T + V into a geodesic Hamiltonian T with one additional degree of freedom, is applied to the four families of…

The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion

- Mathematics
- 2016

In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be…

From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry

- Physics, Mathematics
- 2016

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