A new exactly solvable quantum model in N dimensions
Abstract
The Ndimensional positiondependent mass Hamiltonian Hˆ=ℏ/2(1+λq) ∇+ωq/2(1+λq) is shown to be exactly solvable for any real positive value of the parameter λ. Algebraically, this Hamiltonian can be thought of as a new maximally superintegrable λdeformation of the Ndimensional isotropic oscillator and, from a geometric viewpoint, this system is just the intrinsic oscillator potential on an Ndimensional 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 Ndimensional harmonic oscillator. A further generalization of this construction giving rise to new exactly solvable models is envisaged.
 Publication:

Physics Letters A
 Pub Date:
 March 2011
 DOI:
 10.1016/j.physleta.2011.02.034
 arXiv:
 arXiv:1007.1335
 Bibcode:
 2011PhLA..375.1431B
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 12 pages, 2 figures