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When reading about the hydrogen spectral series (Lyman, Balmer, etc.) I noticed that nowhere are suborbital or sublevels (azimuthal) mentioned; only principal quantum numbers n ....

Are there any p or d orbitals for hydrogen?

If not, aren't jumps from s to s (1s to 2s and back, or 2s to 4s and back, etc.) supposedly 'dipole-forbidden'?

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Are there any p or d orbitals for hydrogen?

Yes, certainly. A generic electronic state for the hydrogen atom is labeled by $n,\ell$, and $m$ (which label the orbital) and $m_s$ (which labels the electron's spin state). However, if we neglect any fine structure effects (e.g. spin-orbit coupling, lamb shift, etc), the energy of an energy eigenstate $|n,\ell,m,m_s\rangle$ is simply given by $-13.6\mathrm{\ eV}/n^2$, so the other quantum numbers are irrelevant.

As you say, however, electric dipole transitions can only occur between certain states - in particular, we have selection rules like $\Delta \ell = \pm 1$, $\Delta m \in\{-1,0,1\}$, and $\Delta s = 0$. Therefore, when you see a dipole transition listed as $2\rightarrow 1$ in terms of the principal quantum number $n$, note that it's leaving out the fact that the only transitions which are consistent with the aforementioned rules are $$|2,1,m,m_s\rangle \mapsto |1,0,0,m_s\rangle$$

That being said, electric dipole transitions are not the only players in the game; higher order effects such as the coupling of the electron spin to the external field expand the space of allowed transitions. Additionally, the addition of fine structure causes the otherwise-degenerate eigenstates for any given $n$ to split slightly, further expanding the complexity of the spectra.

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