Wave packet

A localized disturbance formed by superposing waves with different frequencies or wave numbers. Its shape and motion depend on the component waves and their dispersion.

Superposition principle: A rule stating that overlapping solutions of a linear system combine to form another solution. A packet is built by adding component waves under this rule.
Wavelength: The distance over which a periodic wave repeats its phase. A packet can contain many wavelengths, while its envelope varies over a larger scale.
Quantum mechanics: The physical theory describing matter and radiation through quantized states and probabilistic measurement outcomes. Quantum particles are often represented by localized wave functions assembled from momentum components.
Wave packet spreading: The increase in spatial width of a wave packet as its components propagate at different rates. Dispersion commonly makes initially localized packets broaden over time.
Fourier transform: A mathematical transformation that represents a function as a distribution of frequencies or wave numbers. It links a packet’s spatial shape to its spectrum of components.
Frequency: The number of cycles of a periodic process completed per unit time. A packet’s frequency spread affects its duration and evolution.
Schrödinger equation: The equation governing how a nonrelativistic quantum state changes over time. Its solutions show how a quantum wave packet spreads or propagates.
Heisenberg uncertainty principle: The quantum limit on simultaneously precise position and momentum measurements. A narrow position distribution entails a broad momentum distribution for a quantum packet.
Group velocity: The speed at which the envelope of a wave group or packet propagates. It often describes the packet’s motion when its envelope remains identifiable.
Wave number: A measure of spatial oscillation, equal to 2π divided by wavelength for a sinusoidal wave. Its spread across component waves helps determine a packet’s spatial width.

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Scattering theoryRelated: It models an incident state with finite spatial extent and momentum spread.