Arnold Sommerfeld extended Bohr's model of hydrogen and hydrogen-like atoms by a more sophisticated scheme of quantization. In addition to Bohr's quantization of the azimutal motion (angular momentum) of an electron around the atomic nucleus, Sommerfeld quantized phase integrals for the radial motion (allowing for elliptic orbits) and the orientation of the orbital plane (spatial quantization). Furthermore, he resorted to relativity theory which provided a theory of the fine-structure of atomic spectra. Thus he introduced a new fundamental constant -- "Sommerfeld's fine-structure constant" -- into physics.

Sommerfeld's elaboration paved the way for a broader research effort concerning atomic spectra and quantum theory. The effort started in Sommerfeld's Munich school, but it was soon carried further and involved physicists elsewhere--like Ehrenfest in Leiden, Debye in Göttingen, and Schwarzschild at the front during his service in World War I. The focus of this presentation is on the Munich circle of theorists as an early institutional centre of atomic theory, but this includes a study of how Sommerfeld's activities were perceived elsewhere. Thus it attempts to arrive at a closer insight into the mechanisms at work with the extension of Bohr's theory during the early stages of the path that led to quantum mechanics.