Asymptotic iteration method for the inverse power potentials

The asymptotic iteration method (AIM) is used to accurately calculate the eigenvalues of the Schrödinger equation with the potential ()=−−, ∈(0,1), in arbitrary dimensions. The recently studied case, =1/2, is discussed in detail where we give a reason for non-polynomial solutions. Using AIM sequences, we develop a method to compute the coefficients of the series solution in this case. AIM applications for =1/3,=1/4 and =2/3 are also discussed