Related papers: Study of the Superradiance Phenomenon in the $\alp…
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…
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 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…
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 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…
We figure out the famous Klein's paradox arising from the reflection problem when a Dirac particle encounters a step potential with infinite width. The key is to piecewise solve Dirac equation in such a way that in the region where the…
We investigate the time-evolution problem associated with the Klein-Gordon equation, using superoscillations as initial data. Additionally, the Segal-Bargmann transform is used to derive integral representations of the resulting solutions.
In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to…
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…
In light of the significance of non-commutative quaternionic algebra in modern physics, the current study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing the…
We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of…
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…
Whenever we consider any relativistic quantum wave equation we are confronted with the Klein paradox, which asserts that incident particles will suffer a surplus of reflection when dispersed by a discontinuous potential. Following recent…
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…
Classically, reflectionless kinks transmit all incident radiation. Recently, we have used an analyticity argument together with a solution of the Lippmann-Schwinger equation to write down the leading quantum correction to the reflection…
We consider the relativistic Schr\"odinger (Gordon-Klein) equation with a time dependent vector and a scalar potential on a bounded cylindrical domain. Using a standard Geometric Optics Ansatz, we establish a logarithmic stability estimate…
We derive the Klein--Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein--Gordon equation first using the Einstein…
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…
Here we examine the propagation of relativistic fields in spacetime using the viewpoint applied to derive the Rayleigh--Sommerfeld diffraction integral in three--dimensional space. We use this theory to find the propagators for both the…