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Title: An exactly solvable three-dimensional nonlinear quantum oscillator

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Authors:
 [1] ;  [2]
  1. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
  2. Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
Publication Date:
OSTI Identifier:
22217848
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; BOUND STATE; EIGENFUNCTIONS; EIGENVALUES; ENERGY SPECTRA; EXACT SOLUTIONS; HARMONIC OSCILLATORS; LEGENDRE POLYNOMIALS; NONLINEAR PROBLEMS; OSCILLATORS; S STATES; WAVE FUNCTIONS