Related papers: Space-time evolution of Dirac wave packets
Localization of relativistic particles have been of great research interests over many decades. We investigate the time evolution of the Gaussian wave packets governed by the one dimensional Dirac equation. For the free Dirac equation, we…
This article investigates some solutions of the time-dependent free Dirac equation. Visualizations of these solutions immediately reveal strange phenomena that are caused by the interference of positive- and negative-energy waves. The…
Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic systems is considered. Radial wave packets are constructed from the states of different $n$ quantum number and the same lowest angular…
We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the…
Time evolution of wave packets built from the eigenstates of the Dirac equation for a hydrogenic system is considered. We investigate the space and spin motion of wave packets which, in the non-relativistic limit, are stationary states with…
The dynamics of charge particles described by Gaussian wave packet in monolayer graphene is studied analytically and numerically. We demonstrate that the shape of wave packet at arbitrary time depends on correlation between the initial…
Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
We analyze the trajectories of a massive particle in one space dimension whose motion is guided by a spin-half wave function that evolves according to the free Dirac equation, with its initial wave function being a Gaussian wave packet with…
The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is considered. A comparison to nonrelativistic spin-orbit pendulum effect is discussed. Particular relativistic effects, like Zitterbewegung in spin motion, are found in…
We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory.…
In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long…
For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger…
The worldline of a free electron is revealed by applying Dirac's velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two…
We discuss an extension of the theory of {\em spin-orbit pendulum} phenomenon given in [1] to relativistic approach. It is done within the so called Dirac Oscillator. Our first results, focusing on circular wave packet motion have been…
Classical dynamics of spinning zero-size objects in an external gravitational field is derived from the conservation law of the stress-energy and spin tensors. The resulting world line equations differ from those in the existing literature.…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the…
Wave packets in graphene whose central wave vector is at Dirac points are investigated by numerical calculations. Starting from an initial Gaussian function, these wave packets form into annular peaks that propagate to all directions like…
We investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the well-known spin-orbit…