-- R returns a radial eigenfunction 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 returns a Laguerre function L(x,n,m) = (n + m)! sum(k,0,n,(-x)^k / ((n - k)! (m + k)! k!)) -- print radial eigenfunctions R(1,0) R(2,0) R(2,1) R(3,0) R(3,1) R(3,2) "Verify radial eigenfunctions (1=ok)" rho = r / a0 A = a0^(-3/2) R(1,0) == A 2 exp(-rho) R(2,0) == A sqrt(2)/4 (2 - rho) exp(-rho/2) R(2,1) == A sqrt(6)/12 rho exp(-rho/2) R(3,0) == A 2 sqrt(3)/27 (3 - 2 rho + 2/9 rho^2) exp(-rho/3) R(3,1) == A sqrt(6)/81 rho (4 - 2/3 rho) exp(-rho/3) R(3,2) == A 2 sqrt(30)/1215 rho^2 exp(-rho/3)

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