Editing Wave packet (section)

{{short description|Short "burst" or "envelope" of restricted wave action that travels as a unit}}
{{Redirect|Wave train|the mathematics concept|Periodic travelling wave}}

[[File:Wave packet propagation (phase faster than group, nondispersive).gif|thumb|A looped animation of a wave packet propagating without dispersion: the envelope is maintained even as the phase changes]]

In [[physics]], a '''wave packet''' (also known as a '''wave train''' or '''wave group''') is a short burst of localized wave action that travels as a unit, outlined by an [[Envelope (waves)|envelope]]. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component [[sinusoidal wave]]s of different [[wavenumber]]s, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.<ref>{{Citation
 | title = Quantum Physics: An Introduction
 | author = Joy Manners
 | publisher = CRC Press
 | year = 2000
 | isbn = 978-0-7503-0720-8
 | pages = 53–56
 | url = https://books.google.com/books?id=LkDQV7PNJOMC&dq=wave-packet+wavelengths&pg=PA54
 }}</ref> Any signal of a limited width in time or space requires many frequency components around a center frequency within a [[Bandwidth (signal processing)|bandwidth]] inversely proportional to that width; even a [[gaussian function]] is considered a wave packet because its [[Fourier transform]] is a "packet" of waves of frequencies clustered around a central frequency.<ref>{{Cite web |last=Schwartz |first=Matthew |title=Lecture 11: Wavepackets and dispersion |url=https://scholar.harvard.edu/files/schwartz/files/lecture11-wavepackets.pdf |url-status=live |archive-url=https://web.archive.org/web/20230318213306/https://scholar.harvard.edu/files/schwartz/files/lecture11-wavepackets.pdf |archive-date=2023-03-18 |access-date=2023-06-22 |website=scholar.harvard.edu}}</ref> Each component [[wave function]], and hence the wave packet, are solutions of a [[wave equation]]. Depending on the wave equation, the wave packet's profile may remain constant (no [[#Non-dispersive|dispersion]]) or it may change ([[#Dispersive|dispersion]]) while propagating.