Related papers: Scattering of a scalar relativistic particle by th…
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 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 Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission…
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 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…
In this article, we solved the time--independent one--dimensional Klein--Gordon equation in the presence of $\alpha$--attractor potential using the Log derivative method. We calculated the reflection coefficient $\mathcal{R}$ and the…
In this article, we solve the Duffin--Kemmer--Petiau (DKP) equation in the presence of hyperbolic tangent potential for spin-one particles. By partitioning the spin-one spinor, we show that the DKP equation is equivalent to the…
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…
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 present a new potential barrier that presents the phenomenon of superradiance when the reflection coefficient $R$ is greater than one. We calculated the transmission and reflection coefficients for three different regions. The results…
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…
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…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
One-dimensional scattering problem admitting a complex, PT-symmetric short-range potential V(x) is considered. Using a Runge-Kutta-discretized version of Schroedinger equation we derive the formulae for the reflection and transmission…
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…
The main concepts of the recently developed approach to singular problems of quantum mechanics are extended to the Dirac particle in the Coulomb field of a point-like nucleus with its charge Z>137. The reflection and transmission…
Several physical systems can be treated as a scattering process, and, for these processes, a natural observed quantity arises: the ratio between the reflected and incident intensities, known as the reflection coefficient. This dissertation…
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 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.
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…