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Manipulation and Visualization of Spherical Harmonics in 3D using Mathematica - Prof. Bria, Study notes of Physics

University of Illinois - Urbana-ChampaignPhysics
Prof. Brian L. Demarco

Mathematica code for generating and visualizing spherical harmonics in 3d. It includes various plots such as contourplot3d, densityplot, and manipulate, with adjustable parameters for n, l, and plot range. The code also includes laguerrel functions and abs and sphericalharmonicy functions.

Typology: Study notes

Pre 2010

Uploaded on 03/16/2009

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bg1
ManipulateSphericalPlot3D
Evaluate
AbsSphericalHarmonicYl,m,t,p,
t,0,,p,,, PlotRange 0.5, 0.5,0.5, 0.5,1.1, 1.1,
Mesh False, PlotPoints 36, 18, MaxRecursion ControlActive0, 2,
ViewAngle 0.246, ImageSize 500, 377, Axes False, SphericalRegion True,
Boxed False,
PlotLabel StyleWithll,mRoundm,
TraditionalFormHoldFormrSphericalHarmonicYl,m,,,14,
l,2,"orbital number", 0, 7, 1, Appearance "Labeled",
m,0,"magnetic number",l,l, 1, Appearance "Labeled"
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Download Manipulation and Visualization of Spherical Harmonics in 3D using Mathematica - Prof. Bria and more Study notes Physics in PDF only on Docsity!

Manipulate

SphericalPlot3D

Evaluate

Abs

SphericalHarmonicY

l, m, t, p

t, 0,

p,

, PlotRange

Mesh

False, PlotPoints

, MaxRecursion

ControlActive

ViewAngle

0.246, ImageSize

, Axes

False, SphericalRegion

True,

Boxed

False,

PlotLabel

Style

With

l

l, m

Round

m

TraditionalForm

HoldForm

r

SphericalHarmonicY

l, m,

l, 2, "orbital

number"

, 0, 7, 1, Appearance

"Labeled"

m, 0, "magnetic

number"

l, l, 1, Appearance

"Labeled"

orbital number

3

magnetic number

2

spherical harmonics 3D.nb

Out[1]//TableForm=

4

spherical harmonics 3D.nb

bounds

ContourPlot3D

Evaluate

n

2

n

l

n

n

l

3



n

n

l

LaguerreL

n

l

l

n

Abs

l

m

l

l

m

SphericalHarmonicY

l, m,

n

2, l

1, m

x

2

y

2

z

(^2)

ArcCos

z

x

2

y

2

z

2

ArcTan

x, y

x,

bounds, bounds

y,

bounds, bounds

z,

bounds, bounds

, Contours

1, Mesh

None, ContourStyle

Opacity

, PlotPoints

MaxRecursion

spherical h

bounds

DensityPlot

Evaluate

n

2

n

l

n

n

l

3



n

n

l

LaguerreL

n

l

l

n

Abs

l

m

l

l

m

SphericalHarmonicY

l, m,

n

10, l

7, m

x

2

y

2

z

2

ArcCos

z

x

2

y

2

z

2

ArcTan

x, y

. y

x,

bounds, bounds

z,

bounds, bounds

, PlotPoints

bounds

DensityPlot

Evaluate

n

2

n

l

n

n

l

3



n

n

l

LaguerreL

n

l

l

n

Abs

l

m

l

l

m

SphericalHarmonicY

l, m,

n

10, l

7, m

x

2

y

2

z

2

ArcCos

z

x

2

y

2

z

2

ArcTan

x, y

. z

x,

bounds, bounds

y,

bounds, bounds

, PlotPoints

spherical h

8

spherical harmonics 3D.nb

Manipulate

Plot

n

2

n

l

n

n

l

3



n

n

l

LaguerreL

n

l

l

n

, PlotRange

All,

PlotLabel

"n

ToString

n

"l

ToString

l

n, 1, "principal

n"

, 1, 7, 1, Appearance

"Labeled"

l, 0, "orbital

l"

, 0, n

1, 1, Appearance

"Labeled"

principal n

5

orbital l

4

20

40

60

80

100

μ

10

9

μ

10

9

μ

10

9

μ

10

9

n

5,l

j

10

spherical harmonics 3D.nb

TableForm

Table

Plot

n

2

n

l

n

n

l

3



n

n

l

LaguerreL

n

l

l

n

, PlotRange

All,

PlotLabel

"n

ToString

n

"l

ToString

l

n, 1, 3

l, 0, n

5

10

15

20

25

30

1.41.21.00.80.60.40.

n

1,l

5

10

15

20

25

30

0.15 0.10 0.

n

2,l

5

10

15

20

25

30

0.0120.0100.0080.0060.0040.

n

2,l

5

10

15

20

25

30

0.0250.0200.0150.0100.

n

3,l

5

10

15

20

25

30

0.00100.0005 0.

n

3,l

5

10

15

20

25

30

0.000140.000120.000100.000080.000060.000040.

n

3,l

spherical ha