An accurate zeroth-order perturbation theory for solving power-law potentials within the frame work of the asymptotic iteration method
Faculty of Technology and Applied Sciences, Al-Quds Open University, Nablus, Palestine
2 Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador, A1B 3X7, St. John’s, Canada
3 School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Avenue, C1A 4P3, Charlottetown, PEI, Canada
Accepted: 21 January 2023
Published online: 6 February 2023
Spherically symmetric singular potentials have a wide range of applications, such as molecular and atomic physics. In this work, we present a zeroth-order perturbation theory for solving the Schrödinger equation within the framework of the asymptotic iteration method (AIM). We rely on exponential and hyperbolic potential ansatz substitutions, where the difference between the original and new potential is treated as a small perturbation. Each potential ansatz has a free parameter chosen small enough to give an accurate zeroth order perturbative wave equation solution. This method avoids the oscillatory behavior observed in the asymptotic iteration solutions when applying the AIM to such problems. Finally, we illustrate our approach by solving a few problems, particularly potentials with quartic and sextic singularities. We compared our results with those obtained via other methods and found a good agreement.
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