New features of an asymptotic iteration method for the Dirac equation and their applications

Abstract

We have found that two 'asymptotic' aspects α and β of an asymptotic iteration method for the Dirac equation satisfy nonlinear Riccati equations simultaneously and are reciprocal to each other. By these two properties, we have an insight into this method and reveal why this method can give solutions to the Dirac equation. Furthermore, using the new iteration termination condition expressed by equation ( 15), instead of solving the differential equations directly, we have found exact eigenvalues as well as exact wavefunctions of the Dirac equation with two dimensional Coulomb potential.

Study of a bounded oscillator problem in one dimension

“…In our calculations, we use the asymptotic iteration method (AIM) [29] which has been used for solving secondorder linear and homogenous differential equations [28][29][30][31][32][33][34][35][36][37][38][39][40][41]. This method has been applied to many physical problems [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. The main aim of this paper is to introduce a simple perturbation expansion to calculate the energy eigenvalues.…”

Study of energies spectra and thermodynamic properties of the relativistic Dirac equation using Feynman path integral method

“…Using the Nikiforov-Uvarov method [11][12][13] and supersymmetric quantum mechanics approach [6,14,15], Chen [16] found pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential. Studies of the Dirac equation have been conducted using the Feynman path integral method [17][18][19] and the asymptotic iteration method [20,21]. In this study, we aim to determine the analytical solution of the Dirac equation for equal scalar and vector potentials in the case of a non-zero orbital angular quantum number (l ≠ 0) by making use of the Feynman path integral approach based on the Pöschl-Teller potential.…”

Exact Solutions of D-Dimensional Klein–Gordon Equation with an Energy-Dependent Potential by Using of Nikiforov–Uvarov Method

“…In particular, we encounter energy-dependent potentials either in relativistic or non-relativistic versions of quantum mechanical problems from many areas [24][25][26][27][28][29]. For example, in a relativistic treatment of a point charge in an external Coulomb field described by the Klein-Gordon equation, one encounters wave equations with energy-dependent potentials [30,31].…”