Asymptotic iteration method for eigenvalue problems

Abstract

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y ′′ = λ 0 (x)y ′ + s 0 (x)y is introduced, where λ 0 (x) = 0 and s 0 (x) are C ∞ functions. Applications to Schrödinger type problems, including some with highly singular potentials, are presented.

Lifshitz quasinormal modes and relaxation from holography

“…If for some sufficiently large n 16) one can solve (3.15) and, by plugging this back into (3.14), find a solution for χ(x). This approach is called the Asymptotic Iteration Method and was originally developed by [25]. The Improved Asymptotic Iteration Method entails, as modification to the original approach, some convenient power series expansions of s n and λ n in order to simplify their respective recursive relations.…”

Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

“…The above equation is exactly identical to equation (32) in [31] and so for other values of and after some calculations, one can show that ( ) can be written in terms of the confluent hypergeometric function.…”

“…Here it is necessary to point out that, in the literature, there are many different methods for solving quantum models exactly [32][33][34][35][36]. Boumali and Hassanabadi [31] solved this problem analytically and obtained the exact solutions in terms of the hypergeometric functions.…”

“…Now for clarifying that the wave function obtained from this method is in good agreement with the results of [31], we calculate it for = 2. According to (28) and (32), the three-dimensional invariant subspace is obtained as …”

“…Since the appearance of quantum mechanics, considerable efforts have been devoted to obtaining exact solutions of the relativistic and nonrelativistic wave equations, using different methods and techniques [32][33][34][35][36]. Now in this paper, we study the Dirac oscillator in noncommutative phase space 2 Advances in High Energy Physics within the framework of representation theory of the sl(2) Lie algebra.…”