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.

No abstract

No abstract

No abstract

We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.