Advances in Mathematical Physics
Volume 2011 (2011), Article ID 750168, 20 pages
http://dx.doi.org/10.1155/2011/750168
Research Article

Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

Nasser Saad,1 Richard L. Hall,2 Hakan Çiftçi,3 and Özlem Yesiltas3

1Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PE, Canada C1A 4P3
2Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, QC, Canada H3G 1M8
3Department of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey

Received 11 March 2011; Accepted 13 April 2011

Academic Editor: B. G. Konopelchenko

Copyright © 2011 Nasser Saad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the generalized quantum isotonic oscillator Hamiltonian given by 𝐻 = − 𝑑 2 / 𝑑 𝑟 2 + 𝑙 ( 𝑙 + 1 ) / 𝑟 2 + 𝑤 2 𝑟 2 + 2 𝑔 ( 𝑟 2 − 𝑎 2 ) / ( 𝑟 2 + 𝑎 2 ) 2 , 𝑔 > 0 . Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters 𝑔 , 𝑤 , and 𝑎 may be found to high accuracy.