Study of the generalized quantum isotonic nonlinear oscillator potential
Mathematical Physics
2011-06-21 v1 math.MP
Abstract
We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d^2/dr^2+l(l+1)/r^2+w^2r^2+2g(r^2-a^2)/(r^2+a^2)^2, g>0. Two approaches are explored. A method for finding the quasi-polynomial 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.
Keywords
Cite
@article{arxiv.1104.2591,
title = {Study of the generalized quantum isotonic nonlinear oscillator potential},
author = {Nasser Saad and Richard L. Hall and Hakan Ciftci and Ozlem Yesiltas},
journal= {arXiv preprint arXiv:1104.2591},
year = {2011}
}
Comments
13 pages, 1 figure