Asymptotic Iteration method for singular potentials

Details Asymptotic Iteration method for singular potentials Asymptotic Iteration method for singular potentials

2008-02-14

arxiv.org/abs/0802.2072v1

Int.J.Mod.Phys.A23:1405-1415,2008

Physics

Mathematical Physics

9 pages

Scientific paper

10.1142/S0217751X08039852

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schroedinger equation with the singular potential V(r)=r^2+\lambda/r^\alpha (\alpha,\lambda> 0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials such as V(r) valid for all ranges of coupling \lambda.

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