File:Symmetricwave2.png

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

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Summary[edit]

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

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
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[edit]

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/TimeThumbnailDimensionsUserComment
current13:18, 15 October 2008Thumbnail for version as of 13:18, 15 October 2008600 × 450 (79 KB)TimothyRias (talk | contribs){{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} Category:Physics plots
14:52, 7 October 2008Thumbnail for version as of 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}}-->
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