File:Guassian Dispersion.gif

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Guassian_Dispersion.gif ‎(360 × 223 pixels, file size: 351 KB, MIME type: image/gif, looped, 251 frames)

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Summary

Gaussian wave function allowed to evolve in free space via the Schrödinger equation

generated with Mathematica using the following lines of code: u[x_, t_, x0_, k0_, om_] :=

<code>Exp[-x0^2*k0^2/2]*
 Exp[-(x - I*x0^2*k0)^2/(2*x0^2*(1 + I*om*t))]/
  Sqrt[x0*Sqrt[Pi]*(1 + I*om*t)]</code>

frame[t_] :=

<code>Plot[Abs[u[x, t, 1, 5, 1]]^2, {x, -5, 35}, Axes -> {True, False}, 
 Ticks -> None, PlotRange -> {0, 1/\[Pi]^(1/4)}]</code>

frames = ParallelTable[frame[t], {t, 0, 5, 0.02}];

Export["constant_momentum_wavefunction_in_free_space.gif", frames]

Lua error in package.lua at line 80: module 'strict' not found.

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	11:51, 7 January 2017		360 × 223 (351 KB)	127.0.0.1 (talk)	Gaussian wave function allowed to evolve in free space via the Schrödinger equation <p>generated with Mathematica using the following lines of code: u[x_, t_, x0_, k0_, om_] := </p> <pre><code>Exp[-x0^2k0^2/2] Exp[-(x - Ix0^2k0)^2/(2x0^2(1 + Iomt))]/ Sqrt[x0Sqrt[Pi](1 + Iomt)]</code> </pre> <p>frame[t_] := </p> <pre><code>Plot[Abs[u[x, t, 1, 5, 1]]^2, {x, -5, 35}, Axes -> {True, False}, Ticks -> None, PlotRange -> {0, 1/\[Pi]^(1/4)}]</code> </pre> <p>frames = ParallelTable[frame[t], {t, 0, 5, 0.02}]; </p> Export["constant_momentum_wavefunction_in_free_space.gif", frames]

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