A new exactly solvable quantum model in N dimensions

Abstract

An N-dimensional position-dependent mass Hamiltonian (depending on a parameter λ) 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 λ. Algebraically, this Hamiltonian can be thought of as a new maximally superintegrable λ-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.

12 pages, 2 figures; comments added and typos corrected

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Cited by in corpus (17)

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• Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
• An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
• Jacobi multipliers, non-local symmetries and nonlinear oscillators
• On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
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• Symmetries and integrals of motion of a superintegrable deformed oscillator
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• Exactly solvable deformations of the oscillator and Coulomb systems and their generalization