File:2D Wavefunction (1,1) Surface Plot.png

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Original file (1,575 × 1,181 pixels, file size: 433 KB, MIME type: image/png)

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Description

The quantum wavefunction of a particle in a 2D box of dimensions Lx and Ly. The wavenumbers are:

  • nx=1
  • ny=1
Date
Source Own drawing, plotted in MuPAD.
Author Inductiveload
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions See 2D Quantum Wavefunctions for more plots.

Mathematica Code

[edit]

This code does not require any packages to be loaded. 

nx = 1
ny = 1
Plot3D[
  Sin[nx Pi x]Sin[ny Pi y],
  {x, 0, 1}, 
  {y, 0, 1},
  ImageSize -> 2500,
  BoxRatios -> {2, 2, 2},
  AxesLabel -> {x/Subscript[L, x], y/Subscript[L, y], Subscript[ψ, "1,1"]},
  PlotRange -> {-1, 1},
  TextStyle -> {FontSize -> 96}
  ]

MuPAD Code

[edit]
nx := 1:
ny := 1: 
f := sin(nx*x*PI) * sin(ny*y*PI):

  conts := 16:
  projectionlevel:=-1.5:

colourfunc := zip(RGB::Red, RGB::Yellow,
                  (a, b) -> (f(x,y)+1)/(2)*a
                           -(f(x,y)-1)/(2)*b):

funcplot := plot::Function3d(f(x,y),
                             x = 0..1,
                             y = 0..1,
                             Mesh = [24, 24],
                             Submesh=[8,8],
                             LineColor = RGB::Black.[0.99],
                             LineWidth = 0.15，
                             FillColorFunction = colourfunc,                             
                             AxesTitleFont = ["BKM-cmr17", 20],
                             TicksLabelFont = ["Courier New", 12],                         
                             ViewingBoxZRange = -1.5..1
                            ):

contours := plot::modify(funcplot,
                         ZContours = [Automatic, conts],
                         LineWidth = 0.15,
                         LineColor = RGB::Gray90.[0.5],
                         XLinesVisible = FALSE,
                         YLinesVisible = FALSE,
                         Filled = FALSE
                        ):
                        
projcontours := plot::Transform3d([0, 0, projectionlevel],
                                  [1, 0, 0, 0, 1, 0, 0, 0, 0], 
                                   plot::modify(funcplot, ZContours = [Automatic, conts],
                                                LineWidth = 0.2,
                                                LineColorType = Dichromatic,
                                                LineColor = RGB::Red.[0.99],
                                                LineColor2 = RGB::Yellow.[0.99],
                                                XLinesVisible = FALSE,
                                                YLinesVisible = FALSE,
                                                Filled = FALSE
                                               )
                                  ):
                             
camera := plot::Camera([17, -24, 45],
                       [0.5, 0.4, -0.2],
                       0.038
                      ):
                             
ploteverything := plot::Canvas(funcplot, contours, projcontours,
                               Width = 200*unit::mm, 
                               Height = 150*unit::mm,
                               AxesTitles = ["x/L(x)", "y/L(y)", "z"],                                                              
                               camera
                              ): 
                          
plot(ploteverything)

File history

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Date/TimeThumbnailDimensionsUserComment
current22:36, 4 August 2007Thumbnail for version as of 22:36, 4 August 20071,575 × 1,181 (433 KB)Inductiveload (talk | contribs)
22:31, 4 August 2007Thumbnail for version as of 22:31, 4 August 20071,575 × 1,181 (458 KB)Inductiveload (talk | contribs)
02:03, 19 February 2007Thumbnail for version as of 02:03, 19 February 20071,575 × 1,181 (460 KB)Inductiveload (talk | contribs)Better Proportioned muPAD plot, with better colour scheme
16:53, 18 February 2007Thumbnail for version as of 16:53, 18 February 20071,969 × 1,181 (467 KB)Inductiveload (talk | contribs)mupad plot looks better
04:33, 13 February 2007Thumbnail for version as of 04:33, 13 February 20072,499 × 2,713 (154 KB)Inductiveload (talk | contribs){{Information |Description=The quantum wavefunction of a particle in a 2D box of dimensions L<sub>x</sub> and L<sub>y</sub>. The wavenumbers are: *''n<sub>x</sub>''=1 *''n<sub>y</sub>''=1 |Source=Own drawing, plotted in Mathematica. |Date=13/02/2007 |Au

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