= Spectroscopic origin of the Pauli exclusion principle
In 1925, <Wolfgang Pauli> connected two puzzles: <alkali metal> doublets and their <anomalous Zeeman effect>, and the capacities of closed <electron shells>. His paper assigned the extra two-valued property to the optically active <Electron>, rather than an angular momentum of the closed core. Its <Paschen-Back effect> classification used four <quantum numbers>; these historical labels should not be identified literally with modern $n,\ell,m_\ell,m_s$. The exclusion rule forbade matching all four. This connected resolved one-<Electron> states with closed-group populations. An additional test was the missing triplet counterpart of the equivalent two-$s$-<Electron> <ground state> in <alkaline earth metals>. Pauli explicitly claimed counts of allowed states, not their <energies> or ordering.https://www.chemteam.info/Chem-History/Pauli-1925/Pauli-1925.html[Pauli 1925, §§1–2: four labels, closed groups, exclusion statement and absent triplet s-term; English translation]{ref}
The modern question is especially concrete: if a <Quantum Hamiltonian> has a lowest <one-particle state>, why cannot every <Electron> occupy it? Minimizing <energy> answers which of the allowed <quantum states> is preferred; the <Pauli exclusion principle> determines which <quantum states> are allowed in the first place. <Spectral lines> then test <energy> differences between allowed <multiparticle quantum states>. A line count is not itself a direct count of occupied <spin orbitals>: transitions also depend on <selection rules> and the prepared <quantum state populations>. The observed <anomalous Zeeman effect> supplied constraints for the historical classification; the <two-particle antisymmetrization> below supplies the modern mathematical explanation of exclusion.
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