Wavelength
Wave packets

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. An example is shown in the figure. In general, the envelope of the wave packet moves at a speed different from the constituent waves.

Using Fourier analysis, wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths.

Louis de Broglie postulated that all particles with a specific value of momentum p have a wavelength λ = h / p, where h is the Planck constant. This hypothesis was at the basis of quantum mechanics. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a De Broglie wavelength of about 10 m. To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space. The spatial spread of the wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle.
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