In [this question](https://physics.stackexchange.com/questions/764474/explanation-about-the-rotation-spectrum-from-cold-rm-cs-2-molecules), there is a spectrum exhibiting transitions corresponding to the azimuthal quantum number $\ell$ of a system corresponding to a spinning $\rm{Cs_2}$ molecule.

Regarding hydrogen-like atomcs, I can find spectrum (e.g. [Lyman series](https://en.wikipedia.org/wiki/Lyman_series)) corresponding to transitions of the principal quantum number $n$, but no equivalent for the azimuthal and magnetic quantum numbers $\ell$, $m_l$.

Are there experimental evidences for the quantification of $\ell$, $m_l$ in the case of an hydrogen-like atom?

A link to experimental results exhibiting such quantification would be appreciated.