An exactly-solvable three-dimensional nonlinear quantum oscillator
Abstract
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.
Keywords
Cite
@article{arxiv.1304.3739,
title = {An exactly-solvable three-dimensional nonlinear quantum oscillator},
author = {Axel Schulze-Halberg and John R. Morris},
journal= {arXiv preprint arXiv:1304.3739},
year = {2015}
}