Fayl:Symmetricwave2.png

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Qisqa izoh

Taʼrif
English: Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential.
Manba Oʻzimning ishim
Muallif TimothyRias

Litsenziyalash

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
atribut
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
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  • ulashishga – ishlanmani nusxalash, tarqatish va uzatish
  • remiks qilishga – ishni moslashtirishga
Quyidagi shartlar asosida:
  • atribut – Siz tegishli litsenziyaga havolani taqdim etishingiz va oʻzgartirishlar kiritilganligini koʻrsatishingiz kerak. Siz buni har qanday oqilona yoʻl bilan qilishingiz mumkin, lekin litsenziar Sizni yoki Sizning foydalanishingizni ma'qullashini taklif qiladigan tarzda emas.

Qisqa izoh

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"]

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Sana/VaqtMiniaturaOʻlchamlariFoydalanuvchiIzoh
joriy15:52, 19-Fevral 202415:52, 19-Fevral 2024 dagi versiya uchun tasvir1 811 × 1 356 (540 KB)JähmefyysikkoAntialiasing and higher resolution
13:18, 15-Oktyabr 200813:18, 15-Oktyabr 2008 dagi versiya uchun tasvir600 × 450 (79 KB)TimothyRias{{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} Category:Physics plots
14:52, 7-Oktyabr 200814:52, 7-Oktyabr 2008 dagi versiya uchun tasvir360 × 286 (25 KB)TimothyRias{{Information |Description={{en|1=Symmetric wavefunction}} |Source=Own work by uploader |Author=TimothyRias |Date= |Permission= |other_versions= }} <!--{{ImageUpload|full}}-->

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