Arnold Johannes Wilhelm Sommerfeld (German: [ˈaʁnɔlt ˈzɔmɐˌfɛlt]; born on December 5, 1868, and died on April 26, 1951) was a German theoretical physicist who helped develop atomic and quantum physics. He also taught and guided many students during the new era of theoretical physics.

Sommerfeld helped guide doctoral and postdoctoral students who later became Nobel Prize winners. He worked with at least 30 other well-known scientists, including physicists and chemists.

Sommerfeld helped discover the second quantum number, the azimuthal quantum number, and the third quantum number, the magnetic quantum number. He also introduced the fine-structure constant and helped develop X-ray wave theory.

Early life and education

Arnold Johannes Wilhelm Sommerfeld was born on December 5, 1868, in Königsberg, which is now known as Kaliningrad, Russia. He was born into a family with a long history in Prussia. His mother, Cäcilie Matthias, was born in 1839 and died in 1902. She was the daughter of a builder from Potsdam. His father, Franz Sommerfeld, was a doctor from a prominent family in Königsberg. Arnold’s grandfather had moved to Königsberg from the countryside in 1822 to work as a Court Postal Secretary for the Kingdom of Prussia. Arnold was baptized into the Christian faith in his family’s Prussian Evangelical Protestant Church. Though he was not religious, he never abandoned his Christian beliefs.

Sommerfeld studied mathematics and the physical sciences at the University of Königsberg. His thesis advisor was the mathematician Ferdinand von Lindemann. He also took classes from mathematicians Adolf Hurwitz and David Hilbert, and physicist Emil Wiechert. His involvement in the student group Burschenschaft led to a scar on his face from a duel. He earned his Ph.D. on October 24, 1891.

After completing his doctorate, Sommerfeld stayed at Königsberg to earn his teaching diploma. He passed a national exam in 1892 and then served in the military for one year with a reserve regiment in Königsberg. He finished his required military service in September 1893 and continued to serve voluntarily for eight weeks each year for the next eight years. His appearance, including his mustache, strong build, Prussian manner, and the scar from the duel, made him look like a colonel in the hussars.

Career

In October 1893, Sommerfeld joined the University of Göttingen, which was the main place for mathematics in Germany. There, he worked as an assistant to Theodor Liebisch at the Mineralogical Institute. This opportunity came through a personal connection—Liebisch had been a professor at the University of Königsberg and a friend of the Sommerfeld family.

In September 1894, Sommerfeld became an assistant to Felix Klein. His duties included taking detailed notes during Klein’s lectures, writing them for the Mathematics Reading Room, and managing the room. In 1895, Sommerfeld completed a process called habilitation under Klein, which allowed him to become a Privatdozent at Göttingen. As a Privatdozent, he taught many topics in mathematics and mathematical physics. His lectures on partial differential equations were first given at Göttingen and later became Volume VI of his textbook series Lectures on Theoretical Physics, titled Partial Differential Equations in Physics.

In 1895 and 1896, Klein gave lectures about rotating bodies. These lectures inspired Klein and Sommerfeld to write a four-volume book called Die Theorie des Kreisels. The book took 13 years to complete, from 1897 to 1910. The first two volumes focused on theory, and the last two covered applications in geophysics, astronomy, and technology. Sommerfeld’s work with Klein helped him develop an interest in applied mathematics and improve his teaching skills.

While at Göttingen, Sommerfeld met Johanna Höpfner, the daughter of Ernst Höpfner, who was a curator at Göttingen.

In October 1897, Sommerfeld was appointed Professor of Mathematics at the Bergakademie Clausthal (now Clausthal University of Technology). He was the successor to Wilhelm Wien. This job provided enough income for him to marry Johanna.

At Klein’s request, Sommerfeld became the editor of Volume V of Enzyklopädie der mathematischen Wissenschaften. This was a large task that lasted from 1898 to 1926.

In 1900, Sommerfeld was appointed to the Chair of Applied Mechanics at Technische Hochschule Aachen (now RWTH Aachen University) as an extraordinarius professor. This position was arranged through Klein’s efforts. At Aachen, he developed the theory of hydrodynamics, which interested him for many years. Later, at the University of Munich, his students Ludwig Hopf and Werner Heisenberg wrote their Ph.D. theses on this topic. For his work on journal bearing lubrication during his time at Aachen, he was named one of the 23 “Men of Tribology” by Duncan Dowson.

From 1906, Sommerfeld became Ordinarius Professor of Physics and director of the new Theoretical Physics Institute at the Ludwig-Maximilians-Universität München (LMU Munich). He was chosen for these roles by Wilhelm Röntgen, director of the Physics Institute at Munich, which Sommerfeld saw as being called to a “privileged sphere of action.”

Until the late 19th and early 20th centuries, experimental physics in Germany was considered more important than theoretical physics. However, theorists like Sommerfeld at Munich and Max Born at Göttingen, who had strong mathematical training, changed this. Their work helped make mathematical physics, or theoretical physics, the main focus, while experimental physics was used to test or improve theory. After earning their doctorates with Sommerfeld, Wolfgang Pauli, Werner Heisenberg, and Walter Heitler became Born’s assistants and made major contributions to quantum mechanics, which was rapidly developing at the time.

During his 32 years at Munich, Sommerfeld taught general and specialized courses, as well as seminars and colloquia. General courses covered topics like mechanics, electrodynamics, optics, and partial differential equations in physics. They were held four hours per week for 13 weeks in winter and 11 weeks in summer. These courses were for students who had taken experimental physics courses from Röntgen and later from Wilhelm Wien. Students also had a two-hour weekly session to discuss problems. Specialized courses focused on current topics in theoretical physics and were based on Sommerfeld’s research. These courses later appeared in his scientific publications. The goal was to explore current issues in physics and help students and Sommerfeld gain a deep understanding of them, regardless of whether problems were solved. For seminars and colloquia, students presented papers from recent scientific literature. From 1942 to 1951, Sommerfeld organized his lecture notes for publication. These were published as the six-volume Lectures on Theoretical Physics.

For a list of students, see the list organized by type. Four of Sommerfeld’s doctoral students—Werner Heisenberg, Wolfgang Pauli, Peter Debye, and Hans Bethe—won Nobel Prizes. Others, like Walter Heitler, Rudolf Peierls, and Léon Brill

Works

• Arnold Sommerfeld, "Mathematische Theorie der Diffraction" (The Mathematical Theory of Diffraction), Math. Ann. 47(2–3), pp. 317–374. (1896). doi: 10.1007/bf01447273. Translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri. Published in Mathematical Theory of Diffraction by Birkhäuser Boston in 2003. ISBN: 0-8176-3604-8.
• Arnold Sommerfeld, "Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie" (The Propagation of Waves in Wireless Telegraphy), Ann. Physik [4] 28, 665 (1909); 62, 95 (1920); 81, 1135 (1926).
• Arnold Sommerfeld, "Some Reminiscences of My Teaching Career," American Journal of Physics Volume 17, Number 5, pp. 315–316 (1949). Address given upon receiving the 1948 Oersted Medal.

• Arnold Sommerfeld, Atombau und Spektrallinien (Friedrich Vieweg und Sohn, Braunschweig, 1919). Translated from the third German edition by Henry L. Brose as Atomic Structure and Spectral Lines (Methuen, 1923).
• Arnold Sommerfeld, Three Lectures on Atomic Physics (London: Methuen, 1926).
• Arnold Sommerfeld, Atombau und Spektrallinien, Wellenmechanischer Ergänzungband (Vieweg, Braunschweig, 1929). Title page to Atomic Structure and Spectral Lines (1923), translated by Henry Brose. Translated by Henry L. Brose as Wave-Mechanics: Supplementary Volume to Atomic Structure and Spectral Lines (Dutton, 1929).
• Arnold Sommerfeld, Lectures on Wave Mechanics Delivered before the Calcutta University (Calcutta University, 1929).
• Arnold Sommerfeld and Hans Bethe, Elektronentheorie der Metalle, in H. Geiger and K. Scheel, editors, Handbuch der Physik Volume 24, Part 2, pp. 333–622 (Springer, 1933). Later published as a separate book: Elektronentheorie der Metalle (Springer, 1967).
• Arnold Sommerfeld, Mechanik – Vorlesungen über theoretische Physik Band 1 (Akademische Verlagsgesellschaft Becker & Erler, 1943). Translated from the fourth German edition by Martin O. Stern as Mechanics – Lectures on Theoretical Physics Volume I (Academic Press, 1964).
• Arnold Sommerfeld, Mechanik der deformierbaren Medien – Vorlesungen über theoretische Physik Band 2 (Akademische Verlagsgesellschaft Becker & Erler, 1945). Translated from the second German edition by G. Kuerti as Mechanics of Deformable Bodies – Lectures on Theoretical Physics Volume II (Academic Press, 1964).
• Arnold Sommerfeld, Elektrodynamik – Vorlesungen über theoretische Physik Band 3 (Klemm Verlag, Erscheinungsort, 1948). Translated from the German by Edward G. Ramberg as Electrodynamics – Lectures on Theoretical Physics Volume III (Academic Press, 1964).
• Arnold Sommerfeld, Optik – Vorlesungen über theoretische Physik Band 4 (Dieterich'sche Verlagsbuchhandlung, 1950). Translated from the first German edition by Otto Laporte and Peter A. Moldauer as Optics – Lectures on Theoretical Physics Volume IV (Academic Press, 1964).
• Arnold Sommerfeld, Thermodynamik und Statistik – Vorlesungen über theoretische Physik Band 5, edited by Fritz Bopp and Josef Meixner (Diederichsche Verlagsbuchhandlung, 1952). Edited by F. Bopp and J. Meixner, translated by J. Kestin as *Thermodynamics and Statistical Mechanics – Lectures on Theoretical Physics