Related papers: Diffraction of wave packets in space and time
Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the…
The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous…
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…
Quantum transport in a lattice is distinct from its counterpart in continuum media. Even a free wave packet travels differently in a lattice than in the continuum. We describe quantum scattering in a one dimensional lattice using three…
Negative refraction is a peculiar wave propagation phenomenon that occurs when a wave crosses a boundary between a regular medium and a medium with both constitutive parameters negative at the given frequency. The phase and group velocities…
An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.
Here to represent the propagation of waves I attempted to describe them separately in space and time domains. The time and space wave equations are obtained and investigated, and formulas for the wave propagation are expressed. I also tried…
Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description the effect is time-independent. In the…
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio $\frac{a}{d}$, where $a$ is the characteristic dimension of a small body and $d$ is the distance between neighboring bodies $d =…
Space-time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beam. The ability to manipulate and generate space-time distributions of light has been remarkably enhanced in past few…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…
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…
Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…