File:Spherical harmonics.png: Difference between revisions
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== Summary == | == Summary == | ||
{{ | |||
{{Image_Details | |||
| description = Some illustrative real spherical harmonics | |||
| author = Paul Wormer | |||
| copyright = Paul Wormer | |||
| source = Prepared by the aid of Matlab: | |||
theta = [0:5:180]*pi/180; | theta = [0:5:180]*pi/180; | ||
| Line 66: | Line 65: | ||
title('^cY_3^1=(5cos^2\theta-1)sin\theta cos\phi') | title('^cY_3^1=(5cos^2\theta-1)sin\theta cos\phi') | ||
axis equal off | axis equal off | ||
| date-created = 04/09/2007 | |||
| pub-country = | |||
| notes = | |||
| versions = | |||
}} | |||
== Licensing/Copyright status == | |||
See licensing data below | |||
Revision as of 03:27, 22 June 2009
Summary
| Title / Description
|
Some illustrative real spherical harmonics |
|---|---|
| Author(s)
|
Paul Wormer |
| Copyright holder
|
Paul Wormer See below for license/re-use information. |
| Source
|
Prepared by the aid of Matlab:
theta = [0:5:180]*pi/180; phi = [0:5:360]*pi/180; [Theta, Phi] = meshgrid(theta, phi); H = abs(1);
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,1)
surf(X,Y,Z)
title('Y_0^0 = 1')
axis equal off
H = abs(cos(Theta));
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,2)
surf(X,Y,Z)
title('Y_1^0 = cos\theta')
axis equal off
H = abs(3*cos(Theta).^2-1);
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,3)
surf(X,Y,Z)
title('Y_2^0 = 3cos^2\theta-1')
axis equal off
H = abs(cos(Theta).*sin(Theta).*sin(Phi));
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,4)
surf(X,Y,Z)
title('^sY_2^1 = cos\theta sin\theta sin\phi')
axis equal off
[Theta, Phi] = meshgrid(theta, phi);
H = abs(5*cos(Theta).^3-3*cos(Theta));
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,5)
surf(X,Y,Z)
title('Y_3^0=5cos^3\theta-3cos\theta')
axis equal off
H = abs( (5*cos(Theta).^2-1).*cos(Phi).*sin(Theta) );
X = H.*sin(Theta).*cos(Phi);
Y = H.*sin(Theta).*sin(Phi);
Z = H.*cos(Theta);
subplot(2,3,6)
surf(X,Y,Z)
title('^cY_3^1=(5cos^2\theta-1)sin\theta cos\phi')
axis equal off
|
| Date created
|
04/09/2007 |
| Country of first publication
|
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| Notes
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| Using this image on CZ
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Licensing/Copyright status
See licensing data below
Licensing/Copyright status
Spherical harmonics.png is licenced under the GNU Free Documentation License v1.2 or later
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Read the licence for full details
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Text on the Citizendium is licensed under the Creative Commons Attribution ShareAlike licence.
This media may not be used under those or closely similar terms without separate permission of the copyright holder, or the user's own fair use determination.
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| current | 18:54, 11 March 2022 |  | 1,201 × 900 (59 KB) | Maintenance script (talk | contribs) | == Summary == Importing file |
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