Relativistic spinless particles in the generalized asymmetric Woods–Saxon potential

Abstract

In this study, the Klein–Gordon equation in one spatial dimension is solved exactly for the generalized asymmetric Woods–Saxon potential containing the various forms of physical potentials, such as the usual Woods–Saxon, asymmetric Hulthen, usual Hulthen, asymmetric cusp and usual cusp potentials. The solutions that describe the scattering and bound states of the Klein–Gordon particles are obtained in terms of the hypergeometric functions. Using the boundary conditions satisfied by the wave functions and considering the asymptotic behavior of the wave functions, we examine a condition for the transmission resonances of the relativistic spinless particles in view of the generalized asymmetric Woods–Saxon potential. Furthermore, dependence of the transmission coefficients on the generalized asymmetric Woods–Saxon potential parameters as well as the energies of Klein–Gordon particles is investigated numerically by using the Mathematica Software.