Related papers: Scattering of a Klein-Gordon particle by a Woods-S…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is…
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…
Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a…
The one-dimensional Klein-Gordon equation for equal vector and scalar q-parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in details the solutions of the scattering and bound…
Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we…
We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker $M_{\kappa,\mu}(x)$ function. The reflection and transmission coefficients are calculated in…
We solve the Klein-Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection $R$ and transmission $T$ coefficients are calculated in terms…
In this manuscript, we present analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in $(1+1)$ dimension. In the scattering case, we obtain the…
We solve the Klein-Gordon equation for a step potential with hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection coefficient R and transmission coefficient T are…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
In the previous work, we classified the solutions to a family of systems of Klein-Gordon equations with non-negative energy below the ground state into two parts: one blows up in finite time while the other extends to a global solution. In…
The scattering state solutions of the Klein-Gordon equation with equal scalar and vector Varshni, Hellmann and Varshni-Shukla potentials for any arbitrary angular momentum quantum number l are investigated within the framework of the…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…
The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a…
The scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation we prove the existence of the scattering operator.
We study the scattering problems for the quadratic Klein-Gordon equations with radial initial data in the energy space. For 3D, we prove small data scattering, and for 4D, we prove large data scattering with mass below the ground state.
The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission…
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the…