Asymptotic iteration method for the inverse power potentials

Richard L. Hall; Nasser Saad

doi:10.1140/epjp/s13360-021-01647-x

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2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2021) 136: 688
https://doi.org/10.1140/epjp/s13360-021-01647-x

Regular Article

Asymptotic iteration method for the inverse power potentials

Richard L. Hall¹ and Nasser Saad²^b

¹ Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, H3G 1M8, Quebec, Canada
² School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Avenue, C1A 4P3, Charlottetown, PEI, Canada

^b nsaad@upei.ca

Received: 25 February 2021
Accepted: 5 June 2021
Published online: 24 June 2021

Abstract

The asymptotic iteration method (AIM) is used to accurately calculate the eigenvalues of the Schrödinger equation with the potential $V (r) = - r^{- s}$ $V(r)=-r^{-s}$ , $s \in (0, 1),$ $s\in (0,1),$ in arbitrary dimensions. The recently studied case, $s = 1 / 2$ $$s=1/2$$ , 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 $s = 1 / 3, s = 1 / 4$ $$s=1/3,s=1/4$$ and $s = 2 / 3$ $$s=2/3$$ are also discussed.