Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum

Abstract

The Schrödinger equation with the PT−symmetric Hulthén potential is solved exactly by taking into account effect of the centrifugal barrier for any l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. Our numerical results are in good agreement with the ones obtained before.

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

“…We use the existing approximation for the centrifugal potential term in the non-relativistic model [9,19] which is valid only for value [62,68]:…”

“…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]. Also, other authors have recently proposed an alternative approximation scheme for the centrifugal potential to solve the Schrödinger equation for the Hulthén potential [59].…”

“…Also, other authors have recently proposed an alternative approximation scheme for the centrifugal potential to solve the Schrödinger equation for the Hulthén potential [59]. Taking 1,   their approximation can be reduced to the usual approximation [9,19]. Quite recently, we have also proposed a new approximation scheme for the centrifugal term [13,14].…”