File:Symmetricwave2.png
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Summary
| Description |
English: Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential. |
| Source | Own work |
| Author | TimothyRias |
Licensing
I, the copyright holder of this work, hereby publish it under the following licence:
This file is licensed under the Creative Commons Attribution 3.0 Unported licence.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the licence, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Summary
This 3D graph shows the wavefunction for the 2-particle bosonic state for the one dimensional infinite square well at the same energy as the fermionic 2-particle groundstate. (See for example D.J. Griffiths, Introduction to quantum mechanics, Prentice Hall , 1995, section 5.1.1) The picture was created using Mathematica 6.0 using the following code:
$Assumptions = {n \[Element] Integers, m \[Element] Integers};
f[n_, x_] := Sqrt[2] Sin[n \[Pi] x];
s[n_, m_] :=
Function[{x, y}, (f[n, x] f[m, y] + f[n, y] f[m, x])/Sqrt[2]];
swave2 = Plot3D[Evaluate[-s[3, 1][x, y]], {x, 0, 1}, {y, 0, 1},
PlotPoints -> 35,
PlotRange -> {-2.5, 3.5},
MeshFunctions -> {#3 &},
MeshStyle ->
Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
Mesh -> 10,
ColorFunction -> "LakeColors",
BoxRatios -> {1, 1, .7},
Boxed -> False,
Axes -> False];
sgroundplot = Plot3D[-3, {x, 0, 1}, {y, 0, 1},
MeshFunctions -> {s[1, 3][#1, #2] &},
Mesh -> 10,
MeshStyle ->
Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
PlotPoints -> 50,
ColorFunction -> (ColorData["LakeColors"][(-s[1, 3][#1, #2] + 2.5)/
6] &)];
swave3 = Show[{swave2, sgroundplot},
PlotRange -> {{0, 1}, {0, 1}, {-3, 3}},
Axes -> None,
PlotRangePadding -> None,
ImagePadding -> 1,
FaceGrids -> {
{{-1, 0, 0}, {Table[i, {i, 0, 1, 1/9}],
Table[i, {i, -3, 3, 1}]}},
{{0, -1, 0}, {Table[i, {i, 0, 1, 1/9}], Table[i, {i, -3, 3, 1}]}}
},
ViewPoint -> 1000 {5, 5, 2},
ViewVertical -> {0, 0, 1},
ViewCenter -> {.5, .5, 0},
ImageSize -> 600]
Export["Symmetricwave2.png", swave3, "PNG"]
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:22, 19 February 2024 | | 1,811 × 1,356 (540 KB) | wikimediacommons>Jähmefyysikko | Antialiasing and higher resolution |
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