Radial wavefunction
= Radial wavefunction
{title2=$R_{nl}(r)$}
<Separation of variables> in a <central potential> writes a <wavefunction> as $R_{nl}(r)Y_l^m(\theta,\phi)$. With normalized <spherical harmonics> the radial factor satisfies $\int_0^\infty r^2|R_{nl}|^2dr=1$. The reduced radial function is $u=rR$, with <normalization> $\int|u|^2dr=1$; the two functions have different behavior at the origin. For a regular Coulomb <eigenstate>, $R_{nl}\propto r^l$ near the origin.