Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

Abstract EN

We study the generalized quantum isotonic oscillator Hamiltonian given by H=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)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.