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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.
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.
This wave packet becomes increasingly localized with the addition of many waves. The Fourier transform is a mathematical operation that separates a wave packet into its individual plane waves. The waves shown here are real for illustrative purposes only; in quantum mechanics the wave function is generally complex .
Dispersion occurs when sinusoidal waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave, v {\displaystyle v} , is a function of the wave's wavelength λ {\displaystyle \lambda } :
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.
Localized wave packets, "bursts" of wave action where each wave packet travels as a unit, find application in many fields of physics. A wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called a local wavelength.
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.
Quantum biology is the study of applications of quantum mechanics and theoretical chemistry to aspects of biology that cannot be accurately described by the classical laws of physics. [1] An understanding of fundamental quantum interactions is important because they determine the properties of the next level of organization in biological systems.