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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.
This result is an approximation that fails to capture certain interesting aspects of the evolution a free quantum particle. Notably, the width of the wave packet, as measured by the uncertainty in the position, grows linearly in time for large times. This phenomenon is called the spread of the wave packet for a free particle.
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.
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 physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. [1] The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a ...
A wave packet with dispersion, which causes the group velocity and phase velocity to be different. This image is a 1-dimensional real wave, but electron wave packets are 3-dimensional complex waves. Crystal momentum corresponds to the physically measurable concept of velocity according to [3]: 141
Here ψ is the angle between the path of the wave source and the direction of wave propagation (the wave vector k), and the circles represent wavefronts. Consider one of the phase circles of Fig.12.3 for a particular k , corresponding to the time t in the past, Fig.12.2.
In some (unusual) cases both end points of a branch (family) of periodic travelling wave solutions are homoclinic solutions, [37] in which case one must use an external starting point, such as a numerical solution of the partial differential equations. Periodic travelling wave stability can also be calculated numerically, by computing the spectrum.