File:QM harmonic oscillator time domain.gif
QM_harmonic_oscillator_time_domain.gif (360 × 223 pixels, file size: 246 KB, MIME type: image/gif, looped, 64 frames)
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Summary
[edit]DescriptionQM harmonic oscillator time domain.gif |
English: Time evolution of the probability to find a mass at a position x for a quantum harmonic oscillator. In red the confining potential. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1078025770583445504 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
[edit]m = 1.; \[Omega] = 1.; \[HBar] = 1.; \[Psi][n_, x_] := 1/Sqrt[2^n n!] ((m \[Omega])/(\[Pi] \[HBar]))^(1/4) E^(-((m \[Omega] x^2)/(2 \[HBar]))) HermiteH[n, Sqrt[(m \[Omega])/\[HBar]] x]; \[Lambda][n_] := (2 n + 1) (\[HBar] \[Omega])/2; \[Psi]0[x_] := ( E^(-((x - x0)^2/( 2 \[Sigma]^2)))) /. {x0 -> 3, \[Sigma] -> 0.2} (*initial condition*) nmax = 150; xmin = 2; xmax = 4; xsteps = 1000; c0 = Table[(xmax - xmin)/xsteps* Total[Table[\[Psi]0[x] \[Psi][n, x], {x, xmin, xmax, ( xmax - xmin)/xsteps}]], {n, 1, nmax, 1}]; (*Qick and dirty calculation of the coefficients of the \ expansion over the egigenfunctions. Not perfect but good enough for \ what we need here.*) tmax = 6.3; \[Delta]t = 0.1; evo = Total[ Table[E^(-I \[Lambda][n] t) c0[[n]] Table[\[Psi][n, x], {x, -5, 5, 0.1}], {n, 1, nmax, 1}, {t, 0, tmax, \[Delta]t}]]; dim = Dimensions[evo] p1 = Table[ Show[ Plot[1/(Dimensions[evo][[2]]/ 2)^2 (x - Round[Dimensions[evo][[2]]/2])^2, {x, 1, Dimensions[evo][[2]]}, PlotStyle -> {Thick, Red, Dashed}] , ListPlot[Abs[evo[[j] ]]^2, PlotRange -> {0, 1}, Joined -> True , PlotStyle -> {Black, Thick}] , Axes -> False ] , {j, 1, dim[[1]]}] ListAnimate[p1]
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[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1030470604418428929, was reviewed on 28 December 2018 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.
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