Arnold Johannes Wilhelm Sommerfeld, ForMemRS (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored a large number of students for the new era of theoretical physics. He served as PhD supervisor for more Nobel prize winners in physics than any other supervisor to date.
He introduced the 2nd quantum number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory.
Sommerfeld studied mathematics and physical sciences at the Albertina University of his native city, Königsberg, East Prussia. His dissertation advisor was the mathematician Ferdinand von Lindemann, and he also benefited from classes with mathematicians Adolf Hurwitz and David Hilbert and physicist Emil Wiechert.
His participation in the student fraternity Deutsche Burschenschaft resulted in a fencing scar on his face. He received his Ph.D. in 1891 (age 23).
After receiving his doctorate, Sommerfeld remained at Königsberg to work on his teaching diploma. He passed the national exam in 1892 and then began a year of military service, which was done with the reserve regiment in Königsberg.
He completed his obligatory military service in September 1893, and for the next eight years continued voluntary eight-week military service. With his turned up moustache, his physical build, his Prussian bearing, and the fencing scar on his face, he gave the impression of being a colonel in the hussars.
In October, Sommerfeld went to the University of Göttingen, which was the center of mathematics in Germany. There, he became assistant to Theodor Liebisch, at the Mineralogical Institute, through a fortunate personal contact – Liebisch had been a professor at the University of Königsberg and a friend of the Sommerfeld family.
In September 1894, Sommerfeld became Felix Klein’s assistant, which included taking comprehensive notes during Klein’s lectures and writing them up for the Mathematics Reading Room, as well as managing the reading room. Sommerfeld’s Habilitationsschrift was completed under Klein, in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen.
As a Privatdozent, Sommerfeld lectured on a wide range of mathematical and mathematical physics topics. His lectures on partial differential equations were first offered at Göttingen,and they evolved over his teaching career to become Volume VI of his textbook series Lectures on Theoretical Physics, under the title Partial Differential Equations in Physics.
Lectures by Klein in 1895 and 1896 on rotating bodies led Klein and Sommerfeld to write a four-volume text Die Theorie des Kreisels – a 13-year collaboration, 1897–1910. The first two volumes were on theory, and the latter two were on applications in geophysics, astronomy, and technology. The association Sommerfeld had with Klein influenced Sommerfeld’s turn of mind to be applied mathematics and in the art of lecturing.
While at Göttingen, Sommerfeld met Johanna Höpfner, daughter of Ernst Höpfner, curator at Göttingen. In October, 1897 Sommerfeld began the appointment to the Chair of Mathematics at the Bergakademie in Clausthal-Zellerfeld; he was successor to Wilhelm Wien. This appointment provided enough income to eventually marry Johanna.
At Klein’s request, Sommerfeld took on the position of editor of Volume V of Encyklopädie der mathematischen Wissenschaften; it was a major undertaking which lasted from 1898 to 1926.