How does the anomalous Zeeman formula turn into the normal Zeeman formula in the Paschen-Back limit of strong magnetic fields?
The previous section puts classical physics in a rather positive light. A thoroughly classical picture appears to account for fine structure, normal Zeeman splitting, anomalous Zeeman splitting, and the passage from one to the other as the field strength increases.
On closer examination, we find cracks in the picture. Several non-classical ingredients played a crucial role:
The question of ``stationary'' states comes to the fore when we look at the Paschen-Back effect. Modern progress in chaos theory has clarified the subject further. For weak fields, we have one kind of approximately stationary state (L and S precess about J); for strong fields, a different kind (L and S precess about B.) For intermediate strength fields, the motion becomes chaotic (classically speaking). The Bohr-Sommerfeld quantization procedure throws up its hands when faced with chaotic motion. Yet quantization does not cease when the motion becomes chaotic, as we can tell by gazing at spectral lines.
Quantum mechanics broke the logjam. The stimulus for the fundamental shift in viewpoint did not come from the Zeeman effect, it is true. But the new approach unlocked this and many other mysteries within a year or two.
The next few sections sketch the resolution of these problems. I will do a pretty good job for (1) and (2), an overbrief treatment of (3), but I will barely touch on (4), regretfully leaving the real explanation to the standard textbooks.
© 2001 Michael Weiss