Related papers: Klein paradox for bound states - A puzzling phenom…
In this paper, we have studied the Klein's paradox in the presence of both scalar and vector potential barriers. From the corresponding Dirac equation we have calculated the transmission and reflection coefficients. It is shown that the…
We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis of the scattering of particles in a step potential with an arbitrary mixing of vector and scalar…
We present a resolution of the Klein paradox within the framework of one-particle relativistic quantum mechanics. Not only reflection becomes total but the vacuum remains neutral as well. This is accomplished by replacing the pair…
It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a…
We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the Lagrangian submanifolds of the phase space when…
We discuss the tightly bound (hydrino) solution of the Klein-Gordon equation for the Coulomb potential in 3 dimensions. We show that a similarly tightly bound state occurs for the Dirac equation in 2 dimensions. These states are unphysical…
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 Klein Paradox -- the anomalous scattering of relativistic fermions off a high potential step -- signals the limit of the single-particle interpretation of the Dirac equation. While Quantum Field Theory (QFT) resolves this via pair…
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get…
The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of…
The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the…
In this article we used supersymmetry quantum mechanics and factorization methods to study the bound and scattering state of Klein-Gordon equation with deformed Hulthen plus deformed hyperbolical potential for arbitrary state in…
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…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
A relativistic equation is proposed for the bound state of two particles, which is in accord with the boundary condition for the propagation of the negative-energy states and reduces to the (one-body)Dirac equation in the infinite limit of…
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…
In case of spinless particles there appear additional (singular) solutions in the framework of relativistic Klein-Gordon equation for Coulomb potential. These solutions obey to all requirements of quantum mechanical general principles.…