The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method

Abstract

The bound state solution of the (1+1)-dimensional Klein–Gordon (KG) equation for the generalized Hulthén potential has been studied in the framework of the asymptotic iteration method (AIM). The energy values and the corresponding eigenfunctions are obtained for mixed forms of the Hulthén vector potential and scalar potential.

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

“…Recently, the study of exponential-type potentials has attracted much attention from many authors (for example, cf, ). These physical potentials include the Woods-Saxon [7,8], Hulthén [9][10][11][12][13][14][15][16][17][18][19][20][21][22], modified hyperbolic-type [23], ManningRosen [24][25][26][27][28][29][30][31], the Eckart [32][33][34][35][36][37], the Pöschl-Teller [38] and the Rosen-Morse [39,40] potentials.…”

“…This approximation for the centrifugal potential term [9,19,53] has also been used to solve the Schrödinger equation [9,19], KG [10][11][12][20][21][22] and Dirac equation [20][21][22] for the Hulthén potential. Recently, the KG and Dirac equations have been solved in the presence of the Hulthén potential, where the energy spectrum and the scattering wave functions were obtained for spin-0 and spin-  1 2 particles, using a more general approximation scheme for the centrifugal potential [20][21][22].…”

“…Recently, the KG and Dirac equations have been solved in the presence of the Hulthén potential, where the energy spectrum and the scattering wave functions were obtained for spin-0 and spin-  1 2 particles, using a more general approximation scheme for the centrifugal potential [20][21][22]. They found that the good approximation, however, occurs when the screening parameter  and the dimensionless parameter  are taken as 0.1   and 1,   respectively, which is simply the case of the usual approximation [9,19].…”

An alternative solution of diatomic molecules

“…Among these methods, AIM, which was developed by H. Ciftci in 2003 to solve the Schrödinger like second order differential equation, has been used in many field of physics due to the simplicity in obtaining the energy eigenvalues and corresponding eigenfunctions [35][36][37][38][39][40]. To apply the method, the asymptotic wavefunction form should be proposed after substituting the potential in Schrödinger equations with the AIM then applied to calculate the spectrum of potentials.…”

Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

“…This equation has been addressed for solvable potentials by a number of different methods [19][20][21][22][23][24][25][26][27][28][29][30]. Ciftci et al [31][32][33] recently proposed an alternative method, the asymptotic iteration method (AIM) which draws the attention of a many researchers for relativistic equations [34][35][36][37][38][39][40]. This method has the advantage of obtaining the solution of an eigenvalue problem without needing to obtain a direct solution to the differential equation.…”