Sommerfeld, the son of a physician, was born in Königsberg (now Kaliningrad in Russia) and educated at the university in his native city. He later taught at Göttingen, Clausthal, and Aachen before being appointed to the chair of theoretical physics at the University of Munich in 1906.

In 1916 Sommerfeld produced an important modification to the model of the atom proposed by Niels Bohr in 1913. In Bohr's model an atom consists of a central nucleus around which electrons move in definite circular orbits. The orbits are quantized, that is, the electrons occupy only orbits that have specific energies. The electrons can ‘jump’ to higher or lower levels by either absorbing or emitting photons of the appropriate frequency. It was the emission of just those frequencies that produced the familiar lines of the hydrogen spectrum. Increasing knowledge of the spectrum of hydrogen showed that Bohr's model could not account for the fine structure of the spectral lines. What at first had looked like a single line turned out to be in certain cases a number of lines close to each other. Sommerfeld's solution was to suggest that some of the electrons moved in elliptical rather than circular orbits. This required introducing a second quantum number, the azimuthal quantum number, l, in addition to the principal quantum number of Bohr, n. The two are simply related and together permit the fine structure of atomic spectra to be satisfactorily interpreted.

Sommerfeld was the author of an influential work that went through a number of editions in the 1920s, Atombau und Spektrallinien (Atomic Structure and Spectral Lines).