The eigenfunctions of hydrogen are:

Phi(n, l, m) = (2K)^(3/2) * A(n, l) * p^l * e^ (-p/2) * F(n, l, p) * Y(m, l, Phi, Theta) ;


Phi(n, l, m) = R(n, l, r) * Y(m, l, Phi, Theta);


K = 1/(ao*n) ; (for hydrogen)

p = 2*K*r;

A (n, l) = sqrt ( (n-l-1)! / (2*n*((n+1)!)^3));

n is the principle quantum number, l is the orbital number, m is the spin number all input by the user.

See Legendre for Y (m, l, Phi, Theta) function

See Laguerre for F(n, l, p) function