Related papers: Charges carried by wave packets that are superimpo…
We discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. This refined concept…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
An exact solution of the Dirac equation in the presence of an arbitrary electromagnetic plane wave is found, which corresponds to a focused electron wave packet, with the focus of the wave packet moving at the speed of light in the opposite…
We compute the time evolving probability of a Gaussian wave packet to be reflected from a rectangular potential barrier which is perturbed by reducing its height. A time interval is found during which this probability of reflection is…
The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression…
The energy characteristics of a relativistic charged particle in the field of a plane electromagnetic wave of a given amplitude are studied. The dependence of the particle's energy on its phase coordinate is obtained. The maximum value of…
We consider a charged particle driven by a time-dependent flux threading a quantum ring. The dynamics of the charged particle is investigated using classical treatment, Fourier expansion technique, time-evolution method, and…
We discuss "the plane wave approximation" to quantum mechanical scattering using simple one-dimensional examples. The central points of the paper are that (a) plane waves should be thought of as infinitely wide wave packets, and (b) the…
A model of localized electron wave packets (WPs) with variable position and width (floating and breathing) that are spin-coupled as per the valence-bond theory is presented. It produces accurate potential energy curves of LiH in the ground…
We propose a simple way to determine the periodicities of wave packets in quantum systems directly from the energy differences of the states involved. The resulting classical periods and revival times are more accurate than those obtained…
It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum…
A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This…
The problem of reduction of the wave packet of a relativistic charged particle by emission of a photon is studied with help of the path integral approach. A general expression for arbitrary order correlation function of the electromagnetic…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…
We discuss a simple example demonstrating that spontaneous emission from "space-time-superposed" atomic center-of-mass wave packets is nontrivially and time-dependent modified with respect to the standard dipole-pattern typical of…
We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing…
We study the dynamics of a wavepacket in a potential formed by the sum of a periodic lattice and of a parabolic potential. The dynamics of the wavepacket is essentially a superposition of ``local Bloch oscillations'', whose frequency is…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds}…