Maximal-angular-momentum hydrogen state
= Maximal-angular-momentum hydrogen state
{title2=$R(r)=Ar^l e^{-r/[a(l+1)]}$}
A <hydrogen atom> state with principal quantum number $n=l+1$ has no radial nodes and radial factor $R(r)=Ar^l e^{-r/[a(l+1)]}$, where $a$ is the <Bohr radius>. Its energy is $-\hbar^2/[2ma^2(l+1)^2]$. With unit-normalized <spherical harmonics>, the radial normalization gives $|A|^2=2^{2l+3}/[a^{2l+3}(l+1)^{2l+3}(2l+2)!]$.