= Hydrogen radial wavefunction in the first excited shell
{title2=$R_{20},R_{21}$}
Writing $\rho=r/a_0$, the normalized <radial wavefunctions> are $R_{20}=(2-\rho)e^{-\rho/2}/(2\sqrt2a_0^{3/2})$ and $R_{21}=\rho e^{-\rho/2}/(\sqrt{24}a_0^{3/2})$. Radial <normalization> uses $\int r^2|R|^2dr=1$. The first function has one positive <radial node> at $2a_0$; the second has none. Their behavior at the origin differs from that of the reduced radial function $rR$ and from the <radial probability density> $r^2|R|^2$.
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