File:StationaryStatesAnimation.gif
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StationaryStatesAnimation.gif (300 × 280 pixels, file size: 223 KB, MIME type: image/gif, looped, 41 frames)
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Summary
DescriptionStationaryStatesAnimation.gif |
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 , 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 | |
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]
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20 March 2011
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:21, 20 March 2011 | 300 × 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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