An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric

@article{Ballesteros2014AnES,
  title={An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric},
  author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni},
  journal={arXiv: Mathematical Physics},
  year={2014}
}

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References

SHOWING 1-10 OF 41 REFERENCES

Two kinds of generalized Taub-NUT metrics and the symmetry of associated dynamical systems

A number of researches have been made for the (Euclidean) Taub-NUT metric, because the geodesic for this metric describes approximately the motion of well separated monopole-monopole interaction.

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

Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem

We show that there exist some intimate connections between three unconventional Schrodinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective

Multifold Kepler systems—Dynamical systems all of whose bounded trajectories are closed

According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, an

Superintegrable systems in Darboux spaces

Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of