"Verify linear combinations of spherical harmonic eigenfunctions (1=ok)" Y(l,m) = (-1)^m sqrt((2l + 1)/(4pi) (l - m)!/(l + m)!) * P(expcos(theta),l,m) exp(i m phi) P(f,n,m) = eval(1/(2^n n!) (1 - x^2)^(m/2) * d((x^2 - 1)^n,x,n + m),x,f) -- Laplacian Lap(f) = 1/expsin(theta) d(expsin(theta) d(f,theta),theta) + 1/expsin(theta)^2 d(f,phi,2) c1 = x1 + i y1 c2 = x2 + i y2 c3 = x3 + i y3 c4 = x4 + i y4 c5 = x5 + i y5 "Verify for l=1" psi = c1 Y(1,0) + c2 Y(1,1) + c3 Y(1,-1) -Lap(psi) == 1 (1 + 1) psi "Verify for l=2" psi = c1 Y(2,0) + c2 Y(2,1) + c3 Y(2,2) + c4 Y(2,-1) + c5 Y(2,-2) -Lap(psi) == 2 (2 + 1) psi

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