Related papers: Wath Time an Incident Wave Packet is Reflected?
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
The reflection and transmission of wave functions at a potential step is a well-known issue in a textbook of quantum mechanics. We studied the reflection and transmission characteristics analytically when the potential step is moving at a…
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…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We present a renewed wave-packet analysis based on the following ideas: if a quantum one-particle scattering process and the corresponding state are described by an indivisible wave packet to move as a whole at all stages of scattering,…
We study the evolution of a wave packet impinging onto a one dimensional potential barrier. The transmission and reflection times discussed in the literature for stationary states do not correspond to the times required for the emergence of…
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…
We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially…
The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…
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…
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,…
A modulation of refractive index can move at the speed of light. How it interacts with an electromagnetic wave? Does it reflect? We show that an incident electromagnetic wave, depending on its frequency either is totally transmitted with a…
In this paper we numerically solve the time dependent Schr\"odinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
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 phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
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…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…