A new exactly solvable quantum model with position-dependent mass in N dimensions

Authors:
  • ABAngel Ballesteros
    Angel Ballesteros
  • AEAlberto Enciso
    Alberto Enciso
  • FHFrancisco J. Herranz
    Francisco J. Herranz
  • OROrlando Ragnisco
    Orlando Ragnisco
  • DRDanilo Riglioni
    Danilo Riglioni
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Abstract
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. 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.