An Accurate Zeroth-Order Perturbation Theory for Solving Power-Law Potentials within the Framework of the Asymptotic Iteration Method

Abstract

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 compare our results with those obtained via other methods and find good agreement.

10 pages, 2 figures, 6 tables

References in corpus (11)

• Asymptotic iteration method for eigenvalue problems
• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Spiked harmonic oscillators
• Asymptotic Iteration method for singular potentials
• Generalized spiked harmonic oscillator
• Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model
• Quasi-relativistic harmonic bound states
• Exact solution of the Schrödinger equation with a Lennard-Jones potential
• Spiked oscillators: exact solution
• Bound states of a quartic and sextic inverse-powerlaw potential for all angular momenta
• Finite series representation for the bound states of a spiked isotropic oscillator with inverse-quartic singularity