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on 27 Oct 2021
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N=5; % N>=1
L=4; % 0<=L<=N-1
M=1; % -L<=M<=L, but only use 0<=M<=L
r=meshgrid(0:100);
t=r'/50*pi;
a=N-L-1;
% Short version of laguerre polynomial
F=0;
for i=0:a
F=F+(-1)^i*nchoosek(N+L,a-i)*(2*r/N).^i/prod(1:i);
end
G=legendre(L,cos(t));
P=squeeze(G(1+M,:,:)).*F.*exp(-r/2).*r.^L;
contourf(r.*sin(t),r.*cos(t),abs(P),1e3,'edgec','n');
caxis([0 40]); % Change caxis because P is not normalized
axis equal off;
axis(70*[-1 1 -1 1]);
colormap hot;
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