Circular Coulomb bound state (source code)

= Circular Coulomb bound state

A no-radial-node Coulomb eigenstate has principal quantum number $n=l+1$ and radial factor
$$
R(r)\propto r^l e^{-r/[a(l+1)]}.
$$
Its energy is $-e^2/[8\pi\epsilon_0a(l+1)^2]$.