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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 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.
In 1900, Sommerfeld started his appointment to the Chair of Applied Mechanics at the Königliche Technische Hochschule Aachen (later RWTH Aachen University) 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 University of Munich, Sommerfeld's students Ludwig Hopf and Werner Heisenberg would write their Ph.D. theses on this topic.
From 1906 Sommerfeld established himself as ordinarius professor of physics and director of the new Theoretical Physics Institute at the University of Munich. He was selected for these positions by Wilhelm Röntgen, Director of the Physics Institute at Munich, which was looked upon by Sommerfeld as being called to a "privileged sphere of action."
Up until the late 19th century and early 20th century, experimental physics in Germany was considered as having a higher status within the community. However, in the early 20th century, theorists, such as Sommerfeld at Munich and Max Born at the University of 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.
Over 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.
In 1918, Sommerfeld succeeded Einstein as chair of the Deutsche Physikalische Gesellschaft (DPG). One of his accomplishments was the founding of a new journal. The scientific papers published in DPG journals became so voluminous, a committee of the DPG, in 1919, recommended the establishment of Zeitschrift für Physik for publication of original research articles, which commenced in 1920. Since any reputable scientist could have their article published without refereeing, time between submission and publication was very rapid - as fast as two weeks time. This greatly stimulated the scientific theoretical developments, especially that of quantum mechanics in Germany at that time, as this journal was the preferred publication vehicle for the new generation of quantum theorists with avant-garde views.
In 1928/1929, Sommerfeld traveled around the world with major stops in India, China, Japan, and the United States.
Sommerfeld was a great theoretician, and besides his invaluable contributions to the quantum theory, he worked in other fields of physics, such as the classical theory of electromagnetism. For example, he proposed a solution to the problem of a radiating hertzian dipole over a conducting earth, which over the years led to many applications. His Sommerfeld identity and Sommerfeld integrals are still to the present day the most common way to solve this kind of problem. Also, as a mark of the prowess of Sommerfeld's school of theoretical physics and the rise of theoretical physics in the early 1900s, as of 1928, nearly one-third of the ordinarius professors of theoretical physics in the German-speaking world were students of Sommerfeld.
Arnold Sommerfeld, Stuttgart 1935
On 1 April 1935 Sommerfeld achieved emeritus status, however, he stayed on as his own temporary replacement during the selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of both the Reichserziehungsministerium (REM; Reich Education Ministry) and the supporters of Deutsche Physik, which was anti-Semitic and had a bias against theoretical physics, especially including quantum mechanics. The appointment of Wilhelm Müller - who was not a theoretical physicist, had not published in a physics journal, and was not a member of the Deutsche Physikalische Gesellschaft - as a replacement for Sommerfeld, was considered such a travesty and detrimental to educating a new generation of physicists that both Ludwig Prandtl, director of the Kaiser Wilhelm Institut für Strömungsforschung (Kaiser Wilhelm Institute for Flow Research), and Carl Ramsauer, director of the research division of the Allgemeine Elektrizitäts-Gesellschaft (General Electric Company) and president of the Deutsche Physikalische Gesellschaft, made reference to this in their correspondence to officials in the Reich. In an attachment to Prandtl's 28 April 1941 letter to Reich Marshal Hermann Göring, Prandtl referred to the appointment as "sabotage" of necessary theoretical physics instruction. In an attachment to Ramsauer's 20 January 1942 letter to Reich Minister Bernhard Rust, Ramsauer concluded that the appointment amounted to the "destruction of the Munich theoretical physics tradition".
As for Sommerfeld's once patriotic views, he wrote to Einstein shortly after Hitler took power: "I can assure you that the misuse of the word 'national' by our rulers has thoroughly broken me of the habit of national feelings that was so pronounced in my case. I would now be willing to see Germany disappear as a power and merge into a pacified Europe."
In 2004, the center for theoretical physics at the University of Munich was named after him.
Sommerfeld died in 1951 in Munich from injuries after a traffic accident while walking with his grandchildren.
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 in Mathematical Theory of Diffraction (Birkhäuser Boston, 2003), ISBN0-8176-3604-8
Arnold Sommerfeld, "Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie" (The Propagation of Waves in Wireless Telegraphy), Ann. Physik  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, 315-316 (1949). Address upon receipt of the 1948 Oersted Medal.
Arnold Sommerfeld, Atombau und Spektrallinien (Friedrich Vieweg und Sohn, Braunschweig, 1919)
Arnold Sommerfeld, translated from the third German edition by Henry L. Brose 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)
Arnold Sommerfeld, translated by Henry L. Brose 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, 333-622 (Springer, 1933). This nearly 300-page chapter was 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)
Arnold Sommerfeld, translated from the fourth German edition by Martin O. Stern, 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)
Arnold Sommerfeld, translated from the second German edition by G. Kuerti, 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)
Arnold Sommerfeld, translated from the German by Edward G. Ramberg Electrodynamics - Lectures on Theoretical Physics Volume III (Academic Press, 1964)
Arnold Sommerfeld, Optik - Vorlesungen über theoretische Physik Band 4 (Dieterich'sche Verlagsbuchhandlung, 1950)
Arnold Sommerfeld, translated from the first German edition by Otto Laporte and Peter A. Moldauer Optics - Lectures on Theoretical Physics Volume IV (Academic Press, 1964)
Arnold Sommerfeld, Thermodynamik und Statistik - Vorlesungen über theoretische Physik Band 5 Herausgegeben von Fritz Bopp und Josef Meixner. (Diederich sche Verlagsbuchhandlung, 1952)
Arnold Sommerfeld, edited by F. Bopp and J. Meixner, and translated by J. Kestin, Thermodynamics and Statistical Mechanics - Lectures on Theoretical Physics Volume V (Academic Press, 1964)
Arnold Sommerfeld, Partielle Differentialgleichungen der Physik - Vorlesungen über theoretische Physik Band 6 (Dieterich'sche Verlagsbuchhandlung, 1947)
Arnold Sommerfeld, translated by Ernest G. Straus, Partial Differential Equations in Physics - Lectures on Theoretical Physics Volume VI (Academic Press, first printing 1949, second printing 1953; also as n°1 of AP pure and applied mathematics collection)
Felix Klein and Arnold Sommerfeld, Über die Theorie des Kreisels [4 volumes] (Teubner, 1897)
^The Mathematics Genealogy Project (Arnold SommerfeldArchived 2006-10-17 at the Wayback Machine) 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.
^ abcdeArnold 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.)
^A curator was the resident government representative at the university.
^Jungnickel, 1990b, pp. 274, 277-278, and 281-285.
^Jungnickel, 1990b, pp. 157 - 160, 254 ff., 304 ff., and 384 ff.
^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, especially the postdoctoral students.)
^Eugene Feenberg did doctoral studies with Sommerfeld and completed his Ph.D. in 1933 under Edwin C. Kemble at Harvard University.
^After one year at Munich studying with Sommerfeld, Karl Meissner returned to Tübingen to be able to study spectroscopy with Friedrich Paschen, under whom he received his doctorate in 1915. See: K. W. Meissner reviews: Arnold Sommerfeld, translated from the first German edition by Otto Laporte and Peter A. Moldauer Optics - Lectures on Theoretical Physics Volume IV. American Journal of Physics23 (7) 477-478 (1955). The author states that he attended Sommerfeld's lectures, and specifically on optics, in 1912.
^Through a National Research Council fellowship in 1925-1926 and a Guggenheim Foundation fellowship in 1926-1927, Pauling accomplished postgraduate work with Sommerfeld, Erwin Schrödinger in Zurich, and Niels Bohr in Copenhagen. See: Nobel Prize Biography: PaulingArchived 2007-06-20 at the Wayback Machine. See also: Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics17 315-316 (1949). In the article, Sommerfeld specifically mentions as his (postdoctoral) students the Americans Linus Pauling, Edward U. Condon, and I. I. Rabi.
^After earning his Ph.D. in 1927, Rabi, aided by fellowships, went to Europe for two years to do postgraduate work under Sommerfeld, Niels Bohr, Wolfgang Pauli, Otto Stern, and Werner Heisenberg. See: Isidor Isaac Rabi - BiographicalArchived 2012-10-02 at the Wayback Machine. See also: Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics17 315-316 (1949). In the article, Sommerfeld specifically mentions as his (postdoctoral) students the Americans Linus Pauling, Edward U. Condon, and I. I. Rabi. See also: I. I. Rabi, translated and edited by R. Fraser Code Stories from the early days of quantum mechanics, Physics Today (8) 36-41 (2006). In the article, Rabi comments on his experience as a postdoctoral student of Sommerfeld.
^Walker, 1995, p. 73. Von Laue completed his Habilitation in 1906.
^During the 1930-1931 academic year, Allis spent the first half with Sommerfeld and the last half at the University of Cambridge. He was traveling with Philip M. Morse. See: Philip M. Morse In at the Beginnings: A Physicists Life (MIT Press, second printing 1978) p. 100.
^In 1927 and 1928, Eckart had a Guggenheim Fellowship, which he used to go to Germany to do postgraduate study with Arnold Sommerfeld at the Ludwig Maximilians University of Munich and Werner Heisenberg at the University of Leipzig. Eckart Biography - The National Academies Press and Author Catalog: EckartArchived 2007-02-05 at the Wayback Machine - American Philosophical Society. See also Arnold Sommerfeld, Some Reminiscences of My Teaching Career, American Journal of Physics17 (5) 315-316 (1949).
^Edwin C. Kemble went to Munich and Göttingen in 1927-1928 to study and do research with Sommerfeld and Max Born, respectively.
^In 1927 and 1928, Houston had a Guggenheim Fellowship, which he used to go to Germany to do postgraduate study with Sommerfeld at the Ludwig Maximilians University of Munich and Werner Heisenberg at the University of Leipzig. Houston BiographyArchived 2007-03-24 at the Wayback Machine - The National Academies Press. See also Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics17 (5) 315-316 (1949).
^Paul Kirkpatrick Address of Recommendation by Professor Paul Kirkpatrick, Chairman of the Committee on Awards, American Journal of Physics17 (5) 312-314 (1949). In this article, the following students of Arnold Sommerfeld are mentioned: William V. Houston, Karl Bechert, Otto Scherzer, Otto Laporte, Linus Pauling, Carl Eckart, Gregor Wentzel, Peter Debye, and Philip M. Morse.
^Philip M. Morse In at the Beginnings: A Physicists Life (MIT Press, second printing 1978) p. 100.
^I. I. Rabi, translated and edited by R. Fraser Code Stories from the early days of quantum mechanics, Physics Today (8) 36-41 (2006) p. 38.
^In 1935, the Munich Faculty drew up a candidate list to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics. There were three names on the list: Werner Heisenberg, who received the Nobel Prize in Physics in 1932, Peter Debye, who would receive the Nobel Prize in Chemistry in 1936, and Richard Becker - all former students of Sommerfeld. The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of Deutsche Physik and elements in the Reichserziehungsministerium had their own list of candidates and the battle commenced, dragging on for over four years. During this time, Heisenberg, came under vicious attack by the supporters of Deutsche Physik; one such attack was published in Das Schwarze Korps, the newspaper of the Schutzstaffel, or SS, headed by Heinrich Himmler. At one point, Heisenberg's mother visited Himmler's mother to help bring a resolution to the affair. The two women knew each other as a result of Heisenberg's maternal grandfather and Himmler's father being rectors and members of a Bavarian hiking club. Fortunately, the Heisenberg affair was settled with a victory for academic standards and professionalism, however, with Wilhelm Müller taking over for Sommerfeld on 1 December 1939, it was a political victory over academic standards. See: Beyerchen, 1977, pp. 153-167; Cassidy, 1992, pp 383 - 387; Powers, Thomas, Heisenberg's War: The Secret History of the German Bomb (Knopf, 1993), pp. 40-43; Hentschel, 1996, pp. 176-177; and Goudsmit, Samuel A. ALSOS (Tomash Publishers, 1986) pp 117-119.
Benz, Ulrich, Arnold Sommerfeld. Lehrer und Forscher an der Schwelle zum Atomzeitalter 1868-1951 (Wissenschaftliche Verlagsgesellschaft, 1975)
Beyerchen, Alan D., Scientists Under Hitler: Politics and the Physics Community in the Third Reich (Yale, 1977)
Born, Max, Arnold Johannes Wilhelm Sommerfeld, 1868-1951, Obituary Notices of Fellows of the Royal Society Volume 8, Number 21, pp. 274-296 (1952)
Cassidy, David C., Uncertainty: The Life and Science of Werner Heisenberg (W. H. Freeman and Company, 1992), ISBN0-7167-2503-7 (Since Werner Heisenberg was one of Sommerfeld's Ph.D. students, this is an indirect source of information on Sommerfeld, but the information on him is rather extensive and well documented.)
Eckert, Michael, Arnold Sommerfeld: Atomphysiker und Kulturbote 1868-1951. Eine Biografie (Deutsches Museum, Wallstein Verlag, 2013)
Eckert, Michael, trans. Tom Artin, Arnold Sommerfeld: Science, Life and Turbulent Times, 1868-1951 (Springer, 2013)
Eckert, Michael, Propaganda in science: Sommerfeld and the spread of the electron theory of metals, Historical Studies in the Physical and Biological Sciences Volume 17, Number 2, pp. 191-233 (1987)
Eckert, Michael, Mathematics, Experiments, and Theoretical Physics: The Early Days of the Sommerfeld School, Physics in Perspective Volume 1, Number 3, pp. 238-252 (1999)
Hentschel, Klaus (Editor) and Ann M. Hentschel (Editorial Assistant and Translator), Physics and National Socialism: An Anthology of Primary Sources (Birkhäuser, 1996)
Jungnickel, Christa and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 1: The Torch of Mathematics, 1800 to 1870. University of Chicago Press, paper cover, 1990a. ISBN0-226-41582-1
Jungnickel, Christa and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925. University of Chicago Press, Paper cover, 1990b. ISBN0-226-41585-6
Kant, Horst, Arnold Sommerfeld - Kommunikation und Schulenbildung in Fuchs-Kittowski, Klaus; Laitko, Hubert; Parthey, Heinrich; Umstätter, Walther (editors), Wissenschaft und Digitale Bibliothek: Wissenschaftsforschung Jahrbuch 1998135-152 (Verlag der Gesellschaft für Wissenschaftsforschung, 2000)
Kirkpatrick, Paul, Address of Recommendation by Professor Paul Kirkpatrick, Chairman of the Committee on Awards, American Journal of Physics Volume 17, Number 5, pp. 312-314 (1949). Address preceding award to Arnold Sommerfeld, recipient of the 1948 Oersted Medal for Notable Contributions to the Teaching of Physics, 28 January 1949.
Kragh, Helge, Quantum Generations: A History of Physics in the Twentieth Century (Princeton University Press, fifth printing and first paperback printing, 2002), ISBN0-691-01206-7
Mehra, Jagdish, and Helmut Rechenberg, The Historical Development of Quantum Theory. Volume 1, Part 1, The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld 1900-1925: Its Foundation and the Rise of Its Difficulties. (Springer, 1982), ISBN0-387-95174-1
Pauling, Linus, Arnold Sommerfeld: 1868-1951, Science Volume 114, Number 2963, pp. 383-384 (1951)