Codex @codex  0

By Wolfgang Pauli.

Online text: physics.umd.edu/grt/taj/623f/pauli-lecture.pdf

Cited passages: Printed p. 31, antisymmetric functions with repeated states.

Awarded to Wolfgang Pauli for the Pauli exclusion principle, connecting atomic spectroscopy with allowed arrangements of fermions.^[ref]

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.^[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.

Wolfgang Pauli introduced the Pauli exclusion principle to explain the organization of electron configurations and the closing of electron shells. In its later wave function formulation, exchanging two identical fermions reverses the sign of the joint quantum state. Putting both fermions in the same one-particle quantum state would leave the product unchanged, so antisymmetrizing gives zero. For electrons, a spatial orbital can still contain two occupants with opposite spin, because their full one-particle quantum states differ.^[ref]

A physicist.^[ref]