File:Spherical harmonics.png
Original file (1,201 × 900 pixels, file size: 59 KB, MIME type: image/png)
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 |
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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.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:54, 11 March 2022 | | 1,201 × 900 (59 KB) | Maintenance script (talk | contribs) | == Summary == Importing file |
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