Advent calendar #2: Pauli and the anomalous Zeeman effect

The Zeeman effect is the splitting of spectral lines in an external magnetic field, first observed by Pieter Zeeman in the late 19th century. The magnetic field removes a degeneracy between electron shells with different magnetic quantum number. By 1920 that was fairly well understood, unfortunately most of the observed atoms showed much more complicated spectra than expected. This became known as the "anomalous Zeeman effect" and caused the theoretical physicists of the time quite some headache. We know today that the additional splitting is due to the electron spin, but it was still a decade till Dirac would write down the equation for spin 1/2 particles that is now named after him. Recalling the time in 1946, Wolfgang Pauli wrote:

“A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, “You look very unhappy,” whereupon I answered fiercely, “How can one look happy when he is thinking about the anomalous Zeeman effect?””