ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS

Abstract

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>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 λ.