# File:StationaryStatesAnimation.gif

StationaryStatesAnimation.gif(300 × 280 pixels, file size: 223 KB, MIME type: image/gif, looped, 41 frames)

## Summary

 Description English: Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state ${\displaystyle \psi _{N}=(\psi _{0}+\psi _{1})/{\sqrt {2}}}$, which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called "stationary states".Thus in every quantum stae,there are certain preferred positions of maximum probability Date 20 March 2011 Source Own work Author Sbyrnes321
(* Source code written in Mathematica 6.0 by Steve Byrnes, Feb. 2011. This source code is public domain. *)
(* Shows classical and quantum trajectory animations for a harmonic potential. Assume m=w=hbar=1. *)
ClearAll["Global*"]
(*** Wavefunctions of the energy eigenstates ***)
psi[n_, x_] := (2^n*n!)^(-1/2)*Pi^(-1/4)*Exp[-x^2/2]*HermiteH[n, x];
energy[n_] := n + 1/2;
psit[n_, x_, t_] := psi[n, x] Exp[-I*energy[n]*t];
(*** A non-stationary state ***)
SeedRandom[1];
psinonstationary[x_, t_] := (psit[0, x, t]+psit[1, x, t])/Sqrt[2];

(*** Put all the plots together ***)
SetOptions[Plot, {PlotRange -> {-1, 1}, Ticks -> None, PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Pink]}}];
MakeFrame[t_] := GraphicsGrid[
{{Plot[{Re[psit[0, x, t]], Im[psit[0, x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],0]],
Plot[Abs[psit[0, x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black],
PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],0]]^2]]},
{Plot[{Re[psit[1, x, t]], Im[psit[1, x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],1]],
Plot[Abs[psit[1, x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black],
PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],1]]^2]]},
{Plot[{Re[psinonstationary[x, t]], Im[psinonstationary[x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],N]],
Plot[Abs[psinonstationary[x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black],
PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],N]]^2]]}
}, Frame -> All, ImageSize -> 300];
output = Table[MakeFrame[t], {t, 0, 4 Pi*40/41, 4 Pi/41}];
SetDirectory["C:\\Users\\Steve\\Desktop"]
Export["test.gif", output]
`

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:
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## File history

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Date/TimeThumbnailDimensionsUserComment
current18:21, 20 March 2011300 × 280 (223 KB)Sbyrnes321{{Information |Description ={{en|1=Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the partic
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