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function Ylm = sh(l, m); % function Ylm = sh(l, m); % Draw the equipotential surface of a multipole potential based on % Re Ylm, a spherical harmonic, degree l, order m % Also return numerical values evenly spaced in angle of Re Ylm. n = 6; % Number of samples per half wavelength N = max([30, l*6]); theta = [0 : N]' *pi/N; phi =[-N : N] *pi/N;

% Create the surface of Re Ylm(theta,phi)/r^(l+1) = 1; % Solves for r on a theta, phi grid gamma = 1/(l+1); all = legendre(l, cos(theta)); if (l == 0) all=all'; end % Compensate for error in legendre Ylm = all(m+1, :)' * cos(m*phi); r = abs(Ylm) .^ gamma;

% Convert to Cartesian coordinates X = r.* (sin(theta)*cos(phi)) ; Y = r.* (sin(theta)*sin(phi)); Z = r.* (cos(theta)*ones(size(phi)));

% Color according to size and sign of Ylm C = Ylm;

surf(X, Y, Z, C) axis equal

colormap hot ti=['Surface Y_l^m/r^{l+1}=1 with l=' int2str(l) ', m=' int2str(m)]; title(ti);

the cyclist
on 14 May 2021

Edited: the cyclist
on 14 May 2021

You can run that code by putting it into a file (that would canonically be called sh.m), and then calling that function from the workspace, for example as

l = 2;

m = 1;

Ylm = sh(l,m)

I would recommend calling the function something other than sh, to avoid confusion with shell commands. Also, I recommend against using the variable name all, because that is a MATLAB command.

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