Related papers: QFT Treatment of the Klein Paradox
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…
Reflection and transmission of electrons scattered by a rectangular potential step in the presence of an external magnetic field parallel to the electron beam is described with the use of the Dirac equation. It is shown that in addition to…
The so-called Klein paradox - unimpeded penetration of relativistic particles through high and wide potential barriers - is one of the most exotic and counterintuitive consequences of quantum electrodynamics (QED). The phenomenon is…
It is demonstrated that both transmission and reflection coefficients associated to the Klein paradox at a step barrier are positive and less than unity, so that the particle-antiparticle pair creation mechanism commonly linked to this…
The Dirac equation requires a treatment of the step potential that differs fundamentally from the traditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized by a quantum number with the physical…
The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities'' induced by certain potentials in some regimes of energy. The paradox may be resolved employing the…
The well known Klein paradox for the relativistic Dirac wave equation consists in the computation of possible ``negative probabilities'' induced by certain potentials in some regimes of energy. The paradox may be resolved employing the…
We study the solutions for a one-dimensional electrostatic potential in the Dirac equation when the incoming wave packet exhibits the Klein paradox (pair production). With a barrier potential we demonstrate the existence of multiple…
QFT approaches elaborated for treating quantum effects in time-dependent external electric fields are not directly applicable to time-independent nonuniform electric fields that are given by a step potential and their generalization for the…
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…
The Dirac equation has been applied to fermions scattering from the downward potential step. The results show some particles do not fall off the edge of the step and reflect. Also, based on de Broglie-Bohm interpretation of quantum…
We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…
We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong step-like electric potential in 1+1…
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions…
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…
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…
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast,…
The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein…
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…
The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the…