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

arXiv:1209.0711

Is the Spreading of Quantum Mechanical Wave Packets Indeed Inevitable?

I. Mayer

Published Sep 3, 2012• 0 citations
arXivHTMLPDF

Abstract

It is demonstrated that -- contrary to the common belief -- it is possible to construct solutions of the non-relativistic Schrödinger equation of a free particle, that do not exhibit dispersion. However, it seems that no normalizable wave packets can be built up by their use, so the spreading of the wave packets is indeed inevitable.
DOI
10.48550/arxiv.1209.0711

Related papers

How to build a non-spreading wave packet in quantum mechanics

Stanley A. Bruce

Quantum mechanics asserts that a wave packet must inevitably spread as time progresses since the dispersion relation for the quantum waves is assumed to be quadratic in the momentum k. However, this assumption does not consider the standard frequency Doppler shift formula of Galilean relativity. In this article a non-dispersive wave packet is constructed by appropriately considering the transformation rules between the laboratory and the (particle's) rest inertial reference frames.

arXiv:quant-ph/9905078•May 24, 1999•0 citations

Do free quantum-mechanical wave packets always spread?

James R. Klein

The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is studied, and several results are presented. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Implications for the teaching of quantum mechanics are given.

American Journal of Physics•Dec 1, 1980•20 citations

A particle moving in a homogeneous time-varying force

M. A. Gregório, Antonio S. de Castro

The problem of a quantum-mechanical particle that moves in a spatially uniform time-varying field of force is solved in the Schrödinger picture. An explanation on the peculiar behavior for the spreading of an initial wave packet is given in terms of the dispersion relation obtained in the analytical solution.

American Journal of Physics•Jun 1, 1984•8 citations

Spreading of wave packets in the coordinate representation

Chai Shing Lai

By dealing with the Schrödinger equation for a free particle in the coordinate representation alone, the expression for ψ (r,t) at time t is derived in terms of ψ (r,t0) at an initial instant t0 with the use of the ’’method of self-similar solution of partial differential equations.’’ The use of Green’s function is necessary due to the complex nature of the Schrödinger equation. The same technique can also be applied to the case of spreading of wave packets in a dissipative medium.

American Journal of Physics•Sep 1, 1979•4 citations

Eikonal approximation and the spreading of a wave packet

J. Lerner

Standard eikonal methods, as asymptotic perturbation expansions in 1/\ensuremath{\Elzxh}, are incapable of describing fully the dispersive spreading of a wave packet. By simple models, we distinguish the two types of dispersion associated with a packet having initially uniform and nonuniform distributions of wave number. A nonperturbative extension of the eikonal approximation is applied to two initial-value problems for the free-particle Schr\"odinger equation and compared with exact solutions. The method maintains the ray picture fully. Applications of the method to more general classes of problems are discussed.

Physical Review A•Feb 1, 1986•1 citation

Relativistic suppression of wave packet spreading

Qichang C. Su, B. A. Smetanko, R. Grobe

We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is reduced.

Optics Express•Mar 30, 1998•38 citations
Standard eikonal methods, as asymptotic perturbation expansions in 1/\ensuremath{\Elzxh}, are incapable of describing fully the dispersive spreading of a wave packet. By simple models, we distinguish the two types of dispersion associated with a packet having initially uniform and nonuniform distributions of wave number. A nonperturbative extension of the eikonal approximation is applied to two initial-value problems for the free-particle Schr\"odinger equation and compared with exact solutions. The method maintains the ray picture fully. Applications of the method to more general classes of problems are discussed.