The Asymptotic Iteration Method Revisited

Abstract

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical physics. The analysis and mathematical justifications of the success and failure of the asymptotic iteration method are detailed in this work. A theorem explaining why the asymptotic iteration method works for the eigenvalue problem is presented. As a byproduct, a new procedure to generate unlimited classes of exactly solvable differential equations is also introduced.

11 pages

References in corpus (8)

• Analytical solutions of the Bohr Hamiltonian with the Morse potential
• Criterion for polynomial solutions to a class of linear differential equation of second order
• Asymptotic Iteration method for singular potentials
• Quasi-normal modes for doubly rotating black holes
• Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model
• Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
• Soft and hard confinement of a two-electron quantum system
• Spectra generated by a confined softcore Coulomb potential

Cited by in corpus (3)

• The mathematical foundations of the asymptotic iteration method
• Quantum Information Measures in Quartic and Symmetric Potentials using perturbative approach
• Comment on: "The asymptotic iteration method revisited" [J. Math. Phys. 61, 033501 (2020)]