arXiv:quant-ph/0008107

Diffraction of wave packets in space and time in three dimensions

German Kälbermann

Published Aug 25, 2000• 0 citations

Abstract

A simple formula for the scattering of wave packets from a square well at long times is derived. The expression shows that the phenomenon of wave packet diffraction in space and time exists in three dimensions also. An experiment for the verification of the phenomenon is described and simulated numerically.

DOI: 10.48550/arxiv.quant-ph/0008107

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arXiv:quant-ph/0008107

Diffraction of wave packets in space and time in three dimensions

German Kälbermann

Published Aug 25, 2000• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.quant-ph/0008107

Related papers

Diffraction of wavepackets in space and time

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The phenomenon of wavepacket diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wavepacket quantum scattering off an attractive or repulsive time-independent potential. An analytical formula for the pattern at t →∞ is derived both in one dimension and in three dimensions. The condition for the pattern to exist is developed. The phenomenon is shown numerically and analytically for the Dirac equation in one dimension also. An experiment for the verification of the phenomenon is described and simulated numerically.The phenomenon of wavepacket diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wavepacket quantum scattering off an attractive or repulsive time-independent potential. An analytical formula for the pattern at t →∞ is derived both in one dimension and in three dimensions. The condition for the pattern to exist is developed. The phenomenon is shown numerically and analytically for the Dirac equation in one dimension also. An experiment for the verification of the phenomenon is described and simulated numerically.

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R

and

T

in standard textbook presentations involve an approximation which is almost never discussed. We argue that it should be discussed explicitly, and that doing so provides a simple and intuitively revealing alternative way to derive and understand certain formulas. Using an under-appreciated exact expression for wave packet scattering probabilities, we calculate, for two standard examples, expressions for

R

and

T

for an incident Gaussian wave packet. Comparing these results to the corresponding ones calculated using the plane wave approximation helps illuminate the domain of applicability of that approximation.