We study the generalized quantum isotonic oscillator Hamiltonian given byH=−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 parametersg,w, andamay be found to high accuracy.
The differential-symbol method of constructing the quasipolynomial solutions of two-point in time problem for nonhomogeneous partial differential equation