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    Original file (1,814 × 1,358 pixels, file size: 505 KB, MIME type: image/png)

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    English: Asymmetric wavefunction for a (fermionic) 2-particle state in a one-dimensional square well potential of infinite depth. The 3D graph shows the wavefunction for the 2-particle fermionic first excited state for the square well, with each horizontal axis giving one particle's position.
    Source

    Own work using:

    • See for example: D.J. Griffiths, Introduction to quantum mechanics, Prentice Hall , 1995, section 5.1.1
    • Mathematica 6.0 using the code below
    Author TimothyRias

    Licensing

    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 give appropriate credit, provide a link to the license, 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.

    Code

    &Assumptions = {n \[Element] Integers, m \[Element] Integers};
f[n_, x_] := Sqrt[2] Sin[n \[Pi] x]
a[n_, m_] := Function[{x, y}, (f[n, x] f[m, y] - f[n, y] f[m, x])/Sqrt[2]];
awave2 = Plot3D[Evaluate[a[1, 3][x, y]], {x, 0, 1}, {y, 0, 1},
  PlotPoints -> 35,
  PlotRange -> {-2.5, 3.5},
  MeshFunctions -> {#3 &},
  Mesh -> 10,
  MeshStyle -> 
   Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
  ColorFunction -> "LakeColors",
  BoxRatios -> {1, 1, .7},
  Boxed -> False,
  Axes -> False];
agroundplot = Plot3D[-3, {x, 0, 1}, {y, 0, 1},
  MeshFunctions -> {a[1, 3][#1, #2] &},
  Mesh -> 10,
  MeshStyle -> 
   Directive[ColorData["DeepSeaColors"][.1], Thickness[.002]],
  PlotPoints -> 50,
  ColorFunction -> (ColorData["LakeColors"][(a[1, 3][#1, #2] + 2.5)/
      6] &)
  ];
awave3 = Show[{awave2, agroundplot},
 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["Asymmetricwave2.png", awave3, "PNG"]

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    Date/TimeThumbnailDimensionsUserComment
    current14:58, 4 April 2023Thumbnail for version as of 14:58, 4 April 20231,814 × 1,358 (505 KB)JähmefyysikkoHigher resolution image
    14:51, 4 April 2023Thumbnail for version as of 14:51, 4 April 2023680 × 510 (141 KB)JähmefyysikkoNew rendering with antialiasing (using the same commands)
    13:14, 15 October 2008Thumbnail for version as of 13:14, 15 October 2008600 × 450 (76 KB)TimothyRias{{Information |Description=Asymmetric (fermion) 2-particle state in a infinite square well potential. |Source= |Date= |Author= |Permission= |other_versions= }}
    14:52, 7 October 2008Thumbnail for version as of 14:52, 7 October 2008360 × 286 (24 KB)TimothyRias{{Information |Description={{en|1=Asymmetric wavefunction}} |Source=Own work by uploader |Author=TimothyRias |Date= |Permission= |other_versions= }} <!--{{ImageUpload|full}}-->

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