"Verify normalization of radial eigenfunctions" R(n,l) = 2 / n^2 * a0^(-3/2) * sqrt((n - l - 1)! / (n + l)!) * (2 r / (n a0))^l * L(2 r / (n a0),n - l - 1,2 l + 1) * exp(-r / (n a0)) L(x,n,m) = (n + m)! sum(k,0,n,(-x)^k / ((n - k)! (m + k)! k!)) a0 = 0.529 -- S integrates numerically from 0 to 50 a0 N = 1000 d = 50 a0 / N S(f) = d sum(k,1,N,eval(f,r,(k - 0.5) d)) f = R(1,0)^2 r^2 S(f) f = R(2,0)^2 r^2 S(f) f = R(2,1)^2 r^2 S(f) f = R(3,0)^2 r^2 S(f) f = R(3,1)^2 r^2 S(f) f = R(3,2)^2 r^2 S(f)

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