A new exactly solvable quantum model in N dimensions

@article{Ballesteros2011ANE,
  title={A new exactly solvable quantum model in N dimensions},
  author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni},
  journal={Physics Letters A},
  year={2011},
  volume={375},
  pages={1431-1435}
}

Figures from this paper

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
Exactly solvable deformations of the oscillator and Coulomb systems and their generalization
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
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
The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion
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
Generalized Kaluza–Klein monopole, quadratic algebras and ladder operators
We present a generalized Kaluza–Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger
Position-dependent mass quantum Hamiltonians: General approach and duality
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological
...
...

References

SHOWING 1-10 OF 56 REFERENCES
Supersymmetric approach to quantum systems with position-dependent effective mass
We consider the application of the supersymmetric quantum-mechanical formalism to the Schr\"odinger equation describing a particle characterized by a position-dependent effective mass $m(x).$ We show
Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance
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
Bertrand spacetimes as Kepler/oscillator potentials
Perlick's classification of (3 + 1)-dimensional spherically symmetric and static spacetimes for which the classical Bertrand theorem holds (Perlick V 1992 Class. Quantum Grav. 9 1009) is revisited.
Hamiltonian Systems Admitting a Runge–Lenz Vector and an Optimal Extension of Bertrand’s Theorem to Curved Manifolds
Bertrand’s theorem asserts that any spherically symmetric natural Hamiltonian system in Euclidean 3-space which possesses stable circular orbits and whose bounded trajectories are all periodic is
Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on
...
...