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We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission…
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…
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…
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…
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…
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for…
We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the reflection and transmission coefficients by…
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…
We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulth\'en potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have calculated the…
In this article, we solve the Duffin--Kemmer--Petiau (DKP) equation in the presence of the cusp potential for spin--one particles. We derived the scattering solutions and calculated the bound states in terms of the Whittaker functions. We…
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 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…
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…
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…
We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound…
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…
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…
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…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…