Fitxer:InfiniteSquareWellAnimation.gif
Salta a la navegació
Salta a la cerca
No hi ha cap versió amb una resolució més gran.
InfiniteSquareWellAnimation.gif (300 × 280 píxels, mida del fitxer: 1.006 Ko, tipus MIME: image/gif, en bucle, 139 fotogrames, 14 s)
Resum
| Descripció |
English: Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wavefunction solutions to the Time-Dependent Schrodinger Equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (B,C,D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E,F) are non-stationary states, solutions to the Time-Dependent but not Time-Independent Schrodinger Equation. Both (E) and (F) are randomly-generated superpositions of the four lowest-energy eigenstates, (B-D) plus a fourth not shown. |
| Data | |
| Font | Treball propi |
| Autor | Sbyrnes321 |
(*Source code written in Mathematica 6.0 by Steve Byrnes, Apr. 2011.
This source code is public domain.*)
(*Shows classical and quantum trajectory animations for an infinite-square-well potential.
Assumes L=hbar=1, m=2*pi^(-2), so that the nth energy eigenstate has energy n^2.*)
ClearAll["Global`*"]
(***Wavefunctions of the energy eigenstates***)
psi[n_, x_] := Sin[n*Pi*x]*2^(1/2);
energy[n_] := n^2;
psit[n_, x_, t_] := psi[n, x] Exp[-I*energy[n]*t];
(***A random time-dependent state***)
SeedRandom[1];
CoefList = Table[Random[]*Exp[2*Pi*I*Random[]], {n, 1, 4}];
CoefList = CoefList/Norm[CoefList];
Randpsi[x_, t_] := Sum[CoefList[[n]]*psit[n, x, t], {n, 1, 4}];
(***Another random time-dependent state***)
SeedRandom[2];
CoefList2 = Table[Random[]*Exp[2*Pi*I*Random[]], {n, 1, 3}];
CoefList2 = CoefList2/Norm[CoefList2];
Randpsi2[x_, t_] := Sum[CoefList2[[n]]*psit[n, x, t], {n, 1, 3}];
(***Set default style for plots***)
SetOptions[Plot,
{PlotRange -> {{-.05, 1.05}, {-2.5, 2.5}}, Ticks -> None,
PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Pink]},
Axes -> {True, False}}];
SetOptions[ListPlot, {PlotRange -> {{-.05, 1.05}, {-2.5, 2.5}}, Axes -> False}];
(***Draw walls***)
walls = ListPlot[{{{0, -2.5}, {0, 2.5}}, {{1, -2.5}, {1, 2.5}}},
Joined -> True, PlotStyle -> {{Thick, Black}, {Thick, Black}}];
(***Make the classical plot...a red ball bounces back and forth.***)
classicaltrajectory[t_, left_, right_] := 2*(right - left)*Abs[t - Round[t]] + left;
classicalball[t_, left_, right_] := ListPlot[{{classicaltrajectory[t, left, right], 0}},
PlotStyle -> Directive[Red, AbsolutePointSize[15]]];
classical[t_, label_] := Show[walls, classicalball[t, .1, .9], PlotLabel -> label];
(***Make the quantum plots***)
plotpsi[n_, t_, label_] := Show[walls,
Plot[{Re[psit[n, x, t]], Im[psit[n, x, t]]}, {x, 0, 1}],
PlotLabel -> label, Axes -> {True, False}, Ticks -> None];
plotrand[t_, label_] := Show[walls,
Plot[{Re[Randpsi[x, t]], Im[Randpsi[x, t]]}, {x, 0, 1}],
PlotLabel -> label, Axes -> {True, False}, Ticks -> None];
plotrand2[t_, label_] := Show[walls,
Plot[{Re[Randpsi2[x, t]], Im[Randpsi2[x, t]]}, {x, 0, 1}],
PlotLabel -> label, Axes -> {True, False}, Ticks -> None];
(***Put all the plots together***)
MakeFrame[t_] := GraphicsGrid[
{{classical[3 t/(4 Pi), "A"], plotpsi[1, t, "B"]},
{plotpsi[2, t, "C"], plotpsi[3, t, "D"]},
{plotrand[t, "E"], plotrand2[t, "F"]}},
Frame -> All, ImageSize -> 300];
output = Table[MakeFrame[t], {t, 0, 4 Pi*138/139, 4 Pi/139}];
SetDirectory["C:\\Users\\Steve\\Desktop"]
Export["test.gif", output, "DisplayDurations" -> 10]
Llicència
Jo, el titular dels drets d'autor d'aquest treball, el public sota la següent llicència:
 
|
L'ús d'aquest fitxer és regulat sota les condicions de Creative Commons de CC0 1.0 lliurament al domini públic universal. |
| La persona que ha associat un treball amb aquest document ha dedicat l'obra domini públic, renunciant en tot el món a tots els seus drets de d'autor i a tots els drets legals relacionats que tenia en l'obra, en la mesura permesa per la llei. Podeu copiar, modificar, distribuir i modificar l'obra, fins i tot amb fins comercials, tot sense demanar permís.
|
Historial del fitxer
Cliqueu una data/hora per veure el fitxer tal com era aleshores.
| Data/hora | Miniatura | Dimensions | Usuari/a | Comentari | |
|---|---|---|---|---|---|
| actual | 07:39, 27 abr 2011 | | 300 × 280 (1.006 Ko) | wikimediacommons>Sbyrnes321 | {{Information |Description ={{en|1=Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wav |
Ús del fitxer
La pàgina següent utilitza aquest fitxer:
