Semiclassical measures of eigenfunctions of the attractive Coulomb operator

We characterize the set of semiclassical measures corresponding to sequences of eigenfunctions of the attractive Coulomb operator $\widehat{H}_{\hbar}:=-\frac{\hbar^2}{2}Δ_{\mathbb{R}^3}-\frac{1}{|x|}$. In particular, any Radon probability measure on the fixed negative energy hypersurface $Σ_E$ of t