In this question, 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) 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.

In this question, 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 atoms, I can find spectrum (e.g. 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.