Physics – Quantum Physics
Scientific paper
2010-07-08
Phys.Lett.A375:1431-1435,2011
Physics
Quantum Physics
12 pages, 2 figures; comments added and typos corrected
Scientific paper
10.1016/j.physleta.2011.02.034
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any real positive value of the parameter \lambda. Algebraically, this Hamiltonian can be thought of as a new maximally superintegrable \lambda-deformation of the N-dimensional isotropic oscillator and, from a geometric viewpoint, this system is just the intrinsic oscillator potential on an N-dimensional hyperbolic space with nonconstant curvature. The spectrum of this model is shown to be hydrogenlike, and their eigenvalues and eigenfunctions are explicitly obtained by deforming appropriately the symmetry properties of the N-dimensional harmonic oscillator. A further generalization of this construction giving rise to new exactly solvable models is envisaged.
Ballesteros Angel
Enciso Alberto
Herranz Francisco J.
Ragnisco Orlando
Riglioni Danilo
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