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ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS

Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3, Canada

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RICHARD L. HALL

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

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, and

NASSER SAAD

Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3, Canada

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https://doi.org/10.1142/S0217751X08039852Cited by:38 (Source: Crossref)

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/r^α(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.

Keywords:

PACS: 03.65.Ge

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