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This linear growth is a reflection of the (time-invariant) momentum uncertainty: the wave packet is confined to a narrow Δx = √ a/2, and so has a momentum which is uncertain (according to the uncertainty principle) by the amount ħ/ √ 2a, a spread in velocity of ħ/m √ 2a, and thus in the future position by ħt /m √ 2a. The uncertainty ...
"Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl". The Journal of Chemical Physics. 97 (5).
The atomic wave packet evolves classically for a short period of time and reappears after a classical period. However, after a few classical periods it spreads all over the available space following wave mechanics and collapses. Due to quantum dynamics it rebuilds itself after a certain period of time.
Solitary wave in a laboratory wave channel. In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets.
In fluid dynamics, the Davey–Stewartson equation (DSE) was introduced in a paper by A. Davey and Keith Stewartson to describe the evolution of a three-dimensional wave-packet on water of finite depth.
In physics, a wave packet is a short "burst" or "envelope" of wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.
Wyatt, Robert Eugene; Corey J. Trahan (2005). Quantum dynamics with trajectories.Springer. ISBN 978-0-387-22964-5.; Robert E. Wyatt, Eric R. Bittner: Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids of the amplitude of the wave function, Journal of Chemical Physics, vol. 113, no. 20, 22 November 2000,
Top: plane wave. Bottom: wave packet. When I conceived the first basic ideas of wave mechanics in 1923–1924, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.
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