Study of the generalized quantum isotonic nonlinear oscillator potential

Details Study of the generalized quantum isotonic nonlinear oscillator potential Study of the generalized quantum isotonic nonlinear oscillator potential

2011-04-13

arxiv.org/abs/1104.2591v1

Adv. Math. Phys. 2011 (2011) 750168

Physics

Mathematical Physics

13 pages, 1 figure

Scientific paper

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.

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