Related papers: Once Again On the Klein Paradox
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…
A new exactly solvable relativistic periodic potential is obtained by the periodic extension of a well-known transparent scalar potential. It is found that the energy band edges are determined by a transcendental equation which is very…
The additional hidden symmetry of the Coulomb-Kepler problem is reviewed in classical as well as in quantum mechanics. The main purpose is to elucidate the role of this kind of symmetries in the reduction of physical problems, to show…
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scaterring and the Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of…
We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term…
A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
We extend the $(1+1)$-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component…
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 is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…