Function on_sphere 

pub(crate) fn on_sphere(
    l: i32,
    m: i32,
    unit: [f64; 3],
) -> (Complex, [Complex; 3])

Y = P_l^m(cos theta) exp(i m phi) at a unit vector u and its tangential gradient grad S(u) - l S(u) u, where S is the degree-l solid harmonic with S(u) = Y. The tangential gradient is r times the Cartesian gradient of Y at r u.