Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions

It is shown that, Baire generically, the bound states of the Hamiltonian of the Hydrogen atom have spectral measures with exact $0$-lower and $1\mathrm{/}3$-upper generalized fractal dimensions; the relation to (a weak form of) dynamical delocalization along orthonormal bases is also discussed. Such result is a consequence of the distribution of the Hamiltonian eigenvalues.