wave packet oor Masedonies

wave packet

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en
(physics) a collection of waves, travelling together

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en
short "burst" or "envelope" of localized wave action that travels as a unit
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Gaussian wave packets also are used to analyze water waves.
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Consider a wave packet as a function of position x and time t: α(x,t).
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Assume that the wave packet α is almost monochromatic, so that A(k) is sharply peaked around a central wavenumber k0.
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The figures to the right show how with the addition of many plane waves, the wave packet can become more localized.
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The Schrödinger equation includes the wave function, so its wave packet solution implies the position of a (quantum) particle is fuzzily spread out in wave fronts.
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In representing the wave function of a localized particle, the wave packet is often taken to have a Gaussian shape and is called a Gaussian wave packet.
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Since a wave packet contains a range of different frequencies (and hence different values of k), the group velocity ∂ω/∂k will be different for different values of k.
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The implications are as follows: The motion of a particle, described by a (short-wavelength) wave packet solution to the Schrödinger equation, is also described by the Hamilton–Jacobi equation of motion.
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To localize a particle, de Broglie proposed a superposition of different wavelengths ranging around a central value in a wave packet, a waveform often used in quantum mechanics to describe the wave function of a particle.
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He points out: "If a physical wave field were associated with a particle, or if a particle were identified with a wave packet, then corresponding to N interacting particles there should be N interacting waves in ordinary three-dimensional space.
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Because the virtual quarks are not stable wave packets (quanta), but an irregular and transient phenomenon, it is not meaningful to ask which quark is real and which virtual; only the small excess is apparent from the outside in the form of a hadron.
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It is well known from the theory of Fourier analysis, or from the Heisenberg uncertainty principle (in the case of quantum mechanics) that a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths.
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This causes the wave to display particle-like packets of energy called quanta.
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Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small "packets" or quanta.
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The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and subatomic systems which is today called quantum mechanics.
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