International Journal of Modern Physics E Vol. 15, No. 6 (2006) 1253–1262 c  World Scientiﬁc Publishing Company ACCURATE ITERATIVE AND PERTURBATIVE SOLUTIONS OF THE YUKAWA POTENTIAL M. KARAKOC and I. BOZTOSUN Faculty of Arts and Sciences, Department of Physics, Erciyes University, Kayseri, Turkey Received 7 July 2006 We apply the asymptotic iteration method to solve the radial Schr¨ odinger equation for the Yukawa type potentials. The solution of the radial Schr¨odinger equation by using diﬀerent approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the ﬁndings of the SUSY perturbation, 1/N expansion and numerical methods. Keywords : Yukawa potential; Asymptotic Iteration Method (AIM); bound states; energy eigenvalues; analytical solution; perturbation theory. PACS Numbers: 03.65.Ge 1. Introduction Over the last decades, the energy eigenvalues and corresponding eigenfunctions between interaction systems have raised a great deal of interest in the relativistic as well as in the non-relativistic quantum mechanics. The exact solution of the wave equations (relativistic or non-relativistic) are very important since the wave function contains all the necessary information regarding the quantum system under consideration (for a detailed discussion see Ref. 1 and the references therein). It is well known that the Yukawa potential plays an important role in various branches of physics: In plasma physics, it is known as the Debye-H¨ uckel potential, in solid-state physics and atomic physics, it is called the Thomas-Fermi or the screened Coulomb potential. It is the dominant central part of the nucleon-nucleon interaction arising out of the one-pion-exchange mechanism in nuclear physics. 1,2 It is deﬁned as follows 3 : V (r)= − A r exp (−αr) . (1) 1253