Beschreibung2D Wavefunction (2,2) Surface Plot.png	The quantum wavefunction of a particle in a 2D infinite potential well of dimensions Lx and Ly. The wavenumbers are: nx=2 ny=2 The wavefunction, shown as z on the plot, is given by: ${\displaystyle \psi _{n_{x},n_{y}}=\psi _{0}\sin \left({\frac {n_{x}\pi x}{L}}\right)\sin \left({\frac {n_{y}\pi x}{L}}\right)}$
Datum	13. Februar 2007
Quelle	Own drawing, plotted in MuPad.
Urheber	Inductiveload
Genehmigung (Weiternutzung dieser Datei)	Public domainPublic domainfalsefalse Ich, der Urheberrechtsinhaber dieses Werkes, veröffentliche es als gemeinfrei. Dies gilt weltweit. In manchen Staaten könnte dies rechtlich nicht möglich sein. Sofern dies der Fall ist: Ich gewähre jedem das bedingungslose Recht, dieses Werk für jedweden Zweck zu nutzen, es sei denn, Bedingungen sind gesetzlich erforderlich.
Andere Versionen	See 2D Quantum Wavefunctions for more plots.

Mathematica Code

This code does not require any packages to be loaded.

nx = 3
ny = 2
Plot3D[
  Sin[nx Pi x]Sin[ny Pi y],
  {x, 0, 1}, 
  {y, 0, 1},
  ImageSize -> '''250''',
  BoxRatios -> {2, 2, 2},
  AxesLabel -> {x/Subscript[2L, x], y/Subscript[L, y], Subscript[ψ, "1,1"]},
  PlotRange -> {-1, 1},
  TextStyle -> {FontSize -> 96}
  ]

MuPAD Code

nx := 2:
ny := 2: 
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)