Arnold Johannes Wilhelm Sommerfeld (German: [ˈaʁnɔlt ˈzɔmɐˌfɛlt]; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in both atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics.
Sommerfeld served as doctoral advisor and postdoctoral advisor to seven Nobel Prize winners and supervised at least 30 other famous physicists and chemists.
Sommerfeld introduced the second quantum number, azimuthal quantum number, and the third quantum number, magnetic quantum number. He also introduced the fine-structure constant and pioneered X-ray wave theory.
Arnold Johannes Wilhelm Sommerfeld was born on 5 December 1868 in Königsberg (now Kaliningrad, Russia) into a family with deep ancestral roots in Prussia. His mother, Cäcilie Matthias (1839–1902), was the daughter of a Potsdam builder. His father, Franz Sommerfeld (1820–1906), was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Postal Secretary in the service of the Kingdom of Prussia. Sommerfeld was baptized a Christian in his family's Prussian Evangelical Protestant Church, and although not religious, he would never renounce his Christian faith.
Sommerfeld studied mathematics and physical sciences at the University of Königsberg. His thesis 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 Burschenschaft resulted in a dueling scar on his face. He received his Ph.D. on 24 October 1891.
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 1893, Sommerfeld went to the University of Göttingen, which was the center of mathematics in Germany. There, he became an 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 habilitation was completed under Klein in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen. As a Privatdozent, he 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, the daughter of Ernst Höpfner, curator at Göttingen.
In October 1897, Sommerfeld was appointed Professor of Mathematics at the Bergakademie Clausthal in Saxony; 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 Enzyklopädie der mathematischen Wissenschaften; it was a major undertaking which lasted from 1898 to 1926.
In 1900, Sommerfeld was appointed to the Chair of Applied Mechanics at Technische Hochschule Aachen as extraordinarius professor, which was arranged through Klein's efforts. At Aachen, he developed the theory of hydrodynamics, which would retain his interest for a long time. Later, at the Ludwig-Maximilians-Universität München, Sommerfeld's students Ludwig Hopf and Werner Heisenberg would write their Ph.D. theses on this topic. For his contributions to the understanding of journal bearing lubrication during his time at Technische Hochschule Aachen, he was named as one of the 23 "Men of Tribology" by Duncan Dowson.
From 1906, Sommerfeld established himself as Ordinarius Professor of Physics and director of the new Theoretical Physics Institute at the Ludwig-Maximilians-Universität München. He was selected for these positions by Wilhelm Röntgen, Director of the Physics Institute at the Ludwig-Maximilians-Universität München, which was looked upon by Sommerfeld as being called to a "privileged sphere of action".
Until the late 19th century and early 20th century, experimental physics in Germany was considered as having a higher status within the community. In the early 20th century, theorists, such as Sommerfeld at Munich and Max Born at Göttingen, with their early training in mathematics, turned this around so that mathematical physics, i.e., theoretical physics, became the prime mover, and experimental physics was used to verify or advance theory. After getting their doctorates with Sommerfeld, Wolfgang Pauli, Werner Heisenberg and Walter Heitler became Born's assistants and made significant contributions to the development of quantum mechanics, which was then in very rapid development.
During his 32 years of teaching at Munich, Sommerfeld taught general and specialized courses, as well as holding seminars and colloquia. The general courses were on mechanics, mechanics of deformable bodies, electrodynamics, optics, thermodynamics and statistical mechanics, and partial differential equations in physics. They were held four hours per week, 13 weeks in the winter and 11 weeks in the summer, and were for students who had taken experimental physics courses from Röntgen and later by Wilhelm Wien. There was also a two-hour weekly presentation for the discussion of problems. The specialized courses were of topical interest and based on Sommerfeld's research interests; material from these courses appeared later in the scientific literature publications of Sommerfeld. The objective of these special lectures was to grapple with current issues in theoretical physics and for Sommerfeld and the students to garner a systematic comprehension of the issue, independent of whether or not they were successful in solving the problem posed by the current issue. For the seminar and colloquium periods, students were assigned papers from the current literature and they then prepared an oral presentation. From 1942 to 1951, Sommerfeld worked on putting his lecture notes in order for publication. They were published as the six-volume Lectures on Theoretical Physics.
For a list of students, please see the list organized by type. Four of Sommerfeld's doctoral students, Werner Heisenberg, Wolfgang Pauli, Peter Debye and Hans Bethe, went on to win Nobel Prizes, while others, most notably, Walter Heitler, Rudolf Peierls, Karl Bechert, Hermann Brück, Paul Peter Ewald, Eugene Feenberg, Herbert Fröhlich, Erwin Fues, Ernst Guillemin, Helmut Hönl, Ludwig Hopf, Adolf Kratzer, Otto Laporte, Wilhelm Lenz, Karl Meissner, Rudolf Seeliger, Ernst C. Stückelberg, Heinrich Welker, Gregor Wentzel, Alfred Landé and Léon Brillouin, became famous in their own right. Three of Sommerfeld's postdoctoral supervisees, Linus Pauling, Isidor I. Rabi and Max von Laue, won Nobel Prizes, and ten others, William Allis, Edward Condon, Carl Eckart, Edwin C. Kemble, William V. Houston, Karl Herzfeld, Walther Kossel, Philip M. Morse, Howard Robertson and Wojciech Rubinowicz, went on to become famous in their own right. Walter Rogowski, an undergraduate student of Sommerfeld at Technische Hochschule Aachen, also went on to become famous in his own right. Max Born believed Sommerfeld's abilities included the "discovery and development of talents". Albert Einstein told Sommerfeld: "What I especially admire about you is that you have, as it were, pounded out of the soil such a large number of young talents." Sommerfeld's style as a professor and institute director did not put distance between him and his colleagues and students. He invited collaboration from them, and their ideas often influenced his own views in physics. He entertained them in his home and met with them in cafes before and after seminars and colloquia. Sommerfeld owned an alpine ski hut to which students were often invited for discussions of physics as demanding as the sport.