Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

American Journal of Physics

Spreading Wave Packets—A Cautionary Note

Barry R. Holstein, Arthur R. Swift

Published Jun 1, 1972• 20 citations
Publisher

Abstract

The spreading of a quantum mechanical wave packet is studied from two apparently equivalent points of view. For certain classes of wave functions, one prescription predicts spreading while the other does not. Reasons for this anomaly are discussed.
DOI
10.1119/1.1986678

Related papers

The spreading of free wave packets and the entropy of position

Marian Grabowski

The spreading of free wave packets is expressed by means of the entropy of position for a certain class of states. Connection between such formulation and the usual treatment is discussed.

Journal of Mathematical Physics•Feb 1, 1981•6 citations

Comments on the spreading of a wave packet in quantum mechanics

Stanley A. Bruce

Il Nuovo Cimento B•Sep 1, 1998•0 citations

Spreading of Ultrarelativistic Wave Packet and Redshift

Felix M. Lev

In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.

•Jun 1, 2012•0 citations

Nonspreading wave packets in quantum mechanics

V. K. Ignatovich

Foundations of Physics•Aug 1, 1978•17 citations

Reflections on a Wave Packet Approach to Quantum Mechanical Barrier Penetration

Mark H. Bramhall, Barry M. Casper

We consider the time development of a one-dimensional Gaussian wave packet. Noting that the quantum mechanical predictions concerning position and momentum measurements of a free particle described by a Gaussian packet are consistent with the predictions one would make on the basis of a classical “Naive Model,” we investigate whether this model can account for the scattering of a particle by a rectangular barrier. Obtaining numerical solutions of the time dependent Schrödinger equation for a series of packets with varying incident momenta, we find that the Naive Model is inadequate to explain the quantum mechanical transmission. We study the relative speeds of the transmitted and reflected packets, discussing a number of possible interpretations and indicating the quantum mechanical result. Finally, we note that for certain choices of the parameters describing the packet and the barrier, the reflected packet is composed of two distinct humps.

American Journal of Physics•Sep 1, 1970•29 citations

On the classical limit of the quantum mechanical wave packet

Qian Shang-Wu, Xiang-You Huang

Physics Letters A•Apr 1, 1987•7 citations
In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.
We consider the time development of a one-dimensional Gaussian wave packet. Noting that the quantum mechanical predictions concerning position and momentum measurements of a free particle described by a Gaussian packet are consistent with the predictions one would make on the basis of a classical “Naive Model,” we investigate whether this model can account for the scattering of a particle by a rectangular barrier. Obtaining numerical solutions of the time dependent Schrödinger equation for a series of packets with varying incident momenta, we find that the Naive Model is inadequate to explain the quantum mechanical transmission. We study the relative speeds of the transmitted and reflected packets, discussing a number of possible interpretations and indicating the quantum mechanical result. Finally, we note that for certain choices of the parameters describing the packet and the barrier, the reflected packet is composed of two distinct humps.