Arnold Johannes Wilhelm Sommerfeld (; 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.
Early life and education 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,The Mathematics Genealogy Project (Arnold Sommerfeld ) cites Ferdinand von Lindemann as Sommerfeld's Ph.D. dissertation advisor. Cassidy (Cassidy, 1992, pp. 100 – 101) cites Paul Volkmann as Sommerfeld's advisor and cites a reference. Other authors provide information which can be used to decide between the two, in view of Sommerfeld's abilities. The English translation of Sommerfeld's Habilitationsschrift (Arnold Sommerfeld, translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri Mathematical Theory of Diffraction, Birkhäuser Boston, 2003, pp. 1–2) reveals that Sommerfeld's Ph.D. thesis cited 14 of his teachers at the University of Königsberg and thanked all of them, but particularly named Lindemann in the line of gratitude. Jungnickel (Jungnickel, 1990b, pp. 144–148 and 157–160) is revealing on a number of issues relating to Volkmann. He did little research himself, did not attract physicists, had few publications to his name, and as a physics teacher was a "popularizer". While Sommerfeld attended classes in Volkmann's Theoretical Physics Institute at Königsberg, he looked to Volkmann's assistant Emil Wiechert, rather than Volkmann himself. Sommerfeld was closely associated with Emil Wiechert, who gave him many impressions. Wilfried Schroeder has published the earlier letters between Sommerfeld and Wiechert (Arch. hist. ex. sci., 1984). At the end of the 19th and the early 20th century, there were only four ordinarius professorships for theoretical physics: Königsberg (Volkmann), Göttingen (Woldemar Voigt), Berlin (Max Planck), and Munich, which had been vacant since Ludwig Boltzmann left in 1894, and would not be filled until Sommerfeld was appointed there in 1906. In comments made on the status of theoretical physics in 1899, Voigt only mentioned Planck, Wilhelm Wien, Paul Drude, and Sommerfeld. In a letter to Sommerfeld in 1898, Wien's assessment was similar to Voigt's; Wien only mentioned the chairs at Berlin and Göttingen. Keeping in mind that Munich was unfilled, not mentioning Volkmann's chair at Königsberg to Sommerfeld was a glaring omission, with implications. and he also benefited from classes with mathematicians Adolf Hurwitz and David Hilbert and physicist Emil Wiechert.Mehra, Volume 1, Part 1, 1982, p. 106. His participation in the student fraternity Burschenschaft resulted in a dueling scar on his face.Sommerfeld Biography – MacTutor History of Mathematics He received his Ph.D. on 24 October 1891.Arnold Sommerfeld – Mathematics Genealogy Project. Sommerfeld's Ph.D. thesis title: Die willkürlichen Functionen in der mathematischen Physik.
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.
Career Göttingen In October 1893, Sommerfeld went to the University of Göttingen, which was the center of mathematics in Germany.Arnold Sommerfeld Biography – American Philosophical Society 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.Arnold Sommerfeld, translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri Mathematical Theory of Diffraction (Birkhäuser Boston, 2003),
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 habilitationThe title of Sommerfeld's Habilitation dissertation: Die mathematische Theorie der Beugung was completed under Klein in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen.Sommerfeld-Project – Leibniz-Rechenzentrum der Wissenschaften 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.Arnold Sommerfeld, translated from the fourth German edition by Martin O. Stern Mechanics – Lectures on Theoretical Physics Volume I (Academic Press, 1964), pp. v – x. (Foreword by Paul Peter Ewald and Preface by Sommerfeld.)
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, curatorA curator was the resident government representative at the university. 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.
Aachen 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.
Munich 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,Jungnickel, 1990b, pp. 274, 277–278, and 281–285. 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.Jungnickel, 1990b, pp. 157 – 160, 254 ff., 304 ff., and 384 ff. 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.Cassidy, 1992, p. 104. 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.Sommerfeld's students can be categorized by type, i.e., the course of study under Sommerfeld. (Please see the main text for pertinent footnotes on some students and postdocs.)
Doctoral: Karl Apfelbacher, Hermann Brück, Paul Sophus Epstein, Johannes Fischer, Walter Franz, Herbert Fröhlich, Erwin Fues, Karl Glitscher, Frederick Grover, Ernst Guillemin, Werner Heisenberg, Demetrius Hondros, Helmut Hönl, Ludwig Hopf, Alfred Landé, Herbert Lang, Otto Laporte, Karl Meissner, Josef Meixner, Heinrich Ott, Wolfgang Pauli, Edward Ramberg, Valentin Scheidel, Otto Scherzer, Rudolf Seeliger, Ernst C. Stückelberg and Albrecht Unsöld. Doctoral completing requirements elsewhere: Léon Brillouin, Eugene Feenberg, Rudolf Peierls and Francis G. Slack. Doctoral with Sommerfeld as secondary advisor and the primary advisor annotated in parentheses: Friedrich Burmeister – (Hugo von Seeliger), Walter Heitler – (Karl Herzfeld), Karl Herzfeld – (Friedrich Hasenöhrl), Herman March – (Wilhelm Röntgen), Kurt Urban – (Wilhelm Rabe), Karl Seebach – (Heinrich Tietze) and Bruno Thüring – (Alexander Wilkens). Doctoral and Habilitation: Karl Bechert, Hans Bethe, Peter Debye, Paul Peter Ewald, Adolf Kratzer, Wilhelm Lenz, Ludwig Waldmann, Heinrich Welker and Gregor Wentzel. Habilitation: Walther Kossel, Max von Laue and Wojciech Rubinowicz.