New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces

@article{Ballesteros2011NewSM,
  title={New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces},
  author={{\'A}ngel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco and Danilo Riglioni},
  journal={Journal of Physics: Conference Series},
  year={2011},
  volume={284},
  pages={012011}
}
A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship… 
Massless geodesics in AdS5 × Y (p, q) as a superintegrable system
A bstractA constant of motion of Carter type for a probe particle in the Y (p, q) EinsteinSasaki backgrounds is presented. This quantity is functionally independent with respect to the five known
Position-dependent mass, finite-gap systems, and supersymmetry
The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a
Superintegrable relativistic systems in scalar background fields
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincaré, dilation and special conformal symmetries of the field generate conserved
Energy spectra of position-dependent masses in double heterostructures
We consider position-dependent effective mass particles in double heterostructures, subject to the action of several potentials. A comparative study of the energy spectra of these particles is
Superintegrable systems with position dependent mass
First order integrals of motion for Schrodinger equations with position dependent masses are classified. Eighteen classes of such equations with non-equivalent symmetries are specified. They include

References

SHOWING 1-10 OF 33 REFERENCES
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.
Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces
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.
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
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
Comment on “Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2” [J. Math. Phys. 46, 052702 (2005)]
Carinena, Ranada, and Santander consider a classical Kepler problem in constant curvature spaces and related theory of conics in these spaces. Here we point out that earlier results exist in the
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
An exactly solvable Schrodinger equation with finite positive position-dependent effective mass
The solution of the one-dimensional Schrodinger equation is discussed in the case of position-dependent mass. The general formalism is specified for potentials that are solvable in terms of
...
...