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Asymptotic iteration method for the inverse power potentials

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Abstract

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

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Acknowledgements

The authors would like to thank the reviewer for their constructive comments. Specific regarding the adoption of the criterion (18) that proved to much better approach that the criterion \(|\delta _{m+1}-\delta _m|<\varepsilon \) previous adopted by the present authors. Partial financial support of this work, under Grant No. GP249507 from the Natural Sciences and Engineering Research Council of Canada, is gratefully acknowledged [NS].

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, Quebec, H3G 1M8, Canada

    Richard L. Hall

  2. School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, C1A 4P3, Canada

    Nasser Saad

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  1. Richard L. Hall
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Correspondence to Nasser Saad.

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Hall, R.L., Saad, N. Asymptotic iteration method for the inverse power potentials. Eur. Phys. J. Plus 136, 688 (2021). https://doi.org/10.1140/epjp/s13360-021-01647-x

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