Arnold Sommerfeld attended the Gymnasium in Königsberg. Two slightly older pupils at the same school were Minkowski and Wien. Sommerfeld studied at the University of Königsberg where he was taught by Hilbert, Hurwitz and Lindemann. At this time the University of Königsberg was famous for its school of Theoretical Physics which had been founded by Franz Neumann. However Sommerfeld's interests vere in mathematics rather than physics. In 1891 Sommerfeld was awarded his doctorate from Königsberg.
In 1893 Sommerfeld left Königsberg for Göttingen where he became Klein's assistant. Hurwitz had left Königsberg a year before Sommerfeld and Lindemann left in the same year as Sommerfeld. Two years later Hilbert was to follow Sommerfeld to Göttingen.
At Göttingen, the direction of Sommerfeld's research was immediately influenced by Klein who at this time was heavily involved in applying the theory of functions of a complex variable, and other pure mathematics, to a range of physical topics from astronomy to dynamics. Sommerfeld's first work under Klein's supervision was an impressive piece of work on the mathematical theory of diffraction. His work on this topic contains important theory of partial differential equations.
Other important work which he undertook while at Göttingen included the study of the propogation of electromagnetic waves in wires and the study of the field produced by a moving electron.
From 1897 Sommerfeld taught at Clausthal where he became professor of mathematics at the mining academy. Then, three years later, he became professor of mechanics at the Technische Hochschule of Aachen.
In 1897 he began a 13 year study of gyroscopes woking on a 4 volume work jointly with Klein. In 1906 he became professor of theoretical physics at Munich and worked on atomic spectra. He studied the hypothesis that X-rays were waves and proved this by using crystals as three dimensional diffraction gratings. From 1911 his main area of interest became quantum theory.
Sommerfeld's work led him to replace the circular orbits of the Niels Bohr atom with elliptical orbits; he also introduced the magnetic quantum number in 1916 and, four years later, the inner quantum number. It was theoretical work attempting to explain the inner quantum number that led to the discovery of electron spin.
In the later part of his career, Sommerfeld used statistical mechanics to explain the electronic properties of metals. This replaced an earlier theory due to Lorentz in 1905 based on classical physics. Sommerfeld's approach was to regard electrons in a metal as a degenerate electron gas. He was able to explain features which were unexplained by the earlier classical theory.
Sommerfeld had built up a very famous school of theoretical physics at Munich but its thirty years of fame ended with the Nazi rise to power. In 1940 the school closed but by this time Sommerfeld was 71 years old. He survived World War II only to die in a street accident in Munich.
Bron: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Sommerfeld.html