Wave packet - Revision history

KevinYager: /* Propagation and Interaction */

2014-11-03T13:52:07Z

‎Propagation and Interaction

2014-11-03T13:33:21Z

‎Propagation and Interaction

2014-11-03T13:32:56Z

‎Propagation and Interaction

2014-11-03T13:31:02Z

‎Wave-particle duality

2014-10-13T13:34:58Z

‎Position-momentum tradeoff

2014-10-13T13:34:46Z

‎Position-momentum tradeoff

2014-10-13T13:34:14Z

‎Position-momentum tradeoff

2014-10-13T13:22:21Z

2014-10-12T20:37:57Z

2014-10-11T19:29:33Z

‎See Also

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 ==Wave-particle duality==
 In the context of [[quantum mechanics]], particles can be thought of as wave-packets. That is, quantum particles are neither ideal point-like particles, nor ideal plane-waves. They are instead intermediate objects, which are certainly wave-like (e.g. can undergo interference), but also somewhat localized. The classical concepts of 'particle' (perfectly localized; mathematically a delta-function), and 'wave' (oscillation with a single well-defined wavelength, spread infinitely over all space) can be viewed as limited cases of the general wave-packet. These limiting cases are only conceptual: in reality neither can exist.
 ==Propagation and Interaction==

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 | [[Image:Wavepacket-Box-wavefunc3.gif|500px|thumb|Components of the wavefunction (<math>\scriptstyle \psi(x) </math>) describing a wave-packet bouncing inside a box-like potential. The black line is the real part, and the blue line is the imaginary part.]]
 |-
-| [[Image:Wavepacket-Box-sqr2.gif|500px|thumb|Square of the wavefunction (<math>\scriptstyle | \psi(x) |^2 </math>).]]
+| [[Image:Wavepacket-Box-sqr2.gif|500px|thumb|Square of the wavefunction (<math>\scriptstyle | \psi(x) |^2 </math>) for a wave-packet bouncing inside a box-like potential.]]
 |}

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 {|
-| [[Image:Wavepacket-Box-wavefunc2.gif|500px|thumb|Components of the wavefunction (<math>\scriptstyle \psi(x) </math>) describing a wave-packet bouncing inside a box-like potential. The black line is the real part, and the blue line is the imaginary part.]]
+| [[Image:Wavepacket-Box-wavefunc3.gif|500px|thumb|Components of the wavefunction (<math>\scriptstyle \psi(x) </math>) describing a wave-packet bouncing inside a box-like potential. The black line is the real part, and the blue line is the imaginary part.]]
 |-
 | [[Image:Wavepacket-Box-sqr2.gif|500px|thumb|Square of the wavefunction (<math>\scriptstyle | \psi(x) |^2 </math>).]]

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 In the context of [[quantum mechanics]], particles can be thought of as wave-packets. That is, quantum particles are neither ideal point-like particles, nor ideal plane-waves. They are instead intermediate objects, which are certainly wave-like (e.g. can undergo interference), but also somewhat localized. The classical concepts of 'particle' (perfectly localized; mathematically a delta-function), and 'wave' (oscillation with a single well-defined wavelength, spread infinitely over all space) can be viewed as limited cases of the general wave-packet. These limiting cases are only conceptual: in reality neither can exist.
 ==See Also==
 * [[Fourier transform]]
 * [http://en.wikipedia.org/wiki/Wave_packet Wikipedia: Wave packet]

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 :<math> \tilde{\psi}(k) = \frac{1}{\sqrt{2 \pi}} \int {\psi}(x) e^{-i k x } \mathrm{d}x </math>
 Note that these two descriptions are [[Fourier transform]]s of one another. Thus, there is an inherent tradeoff between the 'spread' of a wave-packet in position-space vs. momentum-space.
-[[Image:Space tradeoff.png|center|thumb|500px|Tradeoff between spread of a wave-packet in position-space (left) and momenum-space (right).]]
+[[Image:Space tradeoff.png|center|thumb|300px|Tradeoff between spread of a wave-packet in position-space (left) and momenum-space (right).]]
 ==Wave-particle duality==

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-A '''wave packet''' is a localized wavelike perturbation.
+A '''wave packet''' is a localized wavelike perturbation, which appears frequently in [[Quantum Mechanics|quantum]] descriptions of particles. For instance, incident [[x-ray]]s during [[scattering]] experiments can be thought of as wave-packets.
-[[File:Wave packet (dispersion).gif|right|thumb|300px|A 1D wave packet (with dispersion), propagating over time.]]
+[[File:Wave packet (dispersion).gif|center|thumb|300px|A 1D wave packet (with dispersion), propagating over time.]]
 ==Wave-particle duality==

← Older revision		Revision as of 20:37, 12 October 2014
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	[[File:2dpack.jpg\|right\|thumb\|300px\|A snapshot of a 2D wave packet.]]		[[File:2dpack.jpg\|right\|thumb\|300px\|A snapshot of a 2D wave packet.]]
		+
		+	==Wave-particle duality==
		+	In the context of [[quantum mechanics]], particles can be thought of as wave-packets. That is, quantum particles are neither ideal point-like particles, nor ideal plane-waves. They are instead intermediate objects, which are certainly wave-like (e.g. can undergo interference), but also somewhat localized. The classical concepts of 'particle' (perfectly localized; mathematically a delta-function), and 'wave' (oscillation with a single well-defined wavelength, spread infinitely over all space) can be viewed as limited cases of the general wave-packet. These limiting cases are only conceptual: in reality neither can exist.