# File:Symmetricwave2.png

Symmetricwave2.png(600 × 450 pixels, file size: 79 KB, MIME type: image/png)

 This physics image could be recreated using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file "Symmetricwave2.svg" - then the template Vector version available (or Vva) does not need the new image name parameter.

## Summary

 Description English: Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential. Date Source Own work Author TimothyRias

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:
 This file is licensed under the Creative Commons Attribution 3.0 Unported license. 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 attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).

## 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

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current13:18, 15 October 2008600 × 450 (79 KB)TimothyRias (talk | contribs){{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} Category:Physics plots
14:52, 7 October 2008360 × 286 (25 KB)TimothyRias (talk | contribs){{Information |Description={{en|1=Symmetric wavefunction}} |Source=Own work by uploader |Author=TimothyRias |Date= |Permission= |other_versions= }} <!--{{ImageUpload|full}}-->
• You cannot overwrite this file.

The following page uses this file:

## File usage on other wikis

The following other wikis use this file:

• Usage on en.wikipedia.org
• Usage on ja.wikipedia.org
• Usage on pa.wikipedia.org
• Usage on pl.wikipedia.org
• Usage on ro.wikipedia.org
• Usage on th.wikipedia.org
• Usage on zh-yue.wikipedia.org
• Usage on zh.wikipedia.org