is it pauli or schrodinger?
is there any original reference?
afaik it was Pauli; he studied the operator algebra of the Hydrogen atom which can be mapped to an SO(4) algebra generated by the angular momentum and the Lenz-Runge operator, from which the spectrum can be derived exactly; however this does not include the solution fort the wave functions
1926, Zeitschrift für Physik, volume 36, page 336
I second Pauli, I remember reading a collection of papers from the beginnings of QM and iirc Pauli did it first.
Schrödinger did it in 1926 too, his paper was received January 27. E. Schrödinger: „Quantisierung als Eigenwertproblem I“, Annalen der Physik 79 (1926).
For Pauli I find "1926, Zeitschrift für Physik, volume 36, page 336-363" with the remark "Abgeschlossen [completed] im Oktober 1925"
It was Pauli, but it doesn't really matter, because the two methods could not have been any more different. It's just like the case of the <Einstein field equations> of GR which were first published by David Hilbert, but the derivation method was different than the method of Einstein.
So the issue of <who was first> is really not that important.
Separate names with a comma.