I have to expand a plane wave in spherical waves by using(adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^{i\vec{k}\cdot\vec{r}}=\sum_{n=0}^{\infty}i^n (2n+1)P_n(cos \theta) j_n(kr)[/tex]

I wrote a matlab code (pasted below) in order to check this by plotting the two sides of the eq above. The graphs are similar but different. I do not know what is wrong with this .... I suppose there are some missing coefficients somewhere....????

clear all;

close all;

clc;

kr=0.1*i+6;

x=linspace(-1, 1, 100);

for(ii=1:100)

F_plane(ii)=exp(i*abs(kr)*x(ii));

end

for(ii=1:100)

F_approx(ii)=0;

for(order=0:150)

ASSOCLEG=legendre(order, x(ii));

F_approx(ii)=F_approx(ii)+i^order*(2*order+1)*besselj(order, abs(kr))*ASSOCLEG(1);

end

end

plot(x, real(F_plane), 'or', x, imag(F_plane), 'ob', x, real(F_approx), '-r', x, imag(F_approx), '-b')

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# Homework Help: Expansion of a plane wave in spherical waves

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