Arnold Sommerfeld Explained

Arnold Sommerfeld
Birth Date:	5 December 1868
Birth Place:	Königsberg, Kingdom of Prussia
Death Place:	Munich, West Germany
Field:	Physics
Workplaces:	University of Göttingen Technische Universität Clausthal University of Aachen University of Munich
Thesis Title:	The arbitrary functions in mathematical physics
Thesis Year:	1891
Alma Mater:	University of Königsberg
Doctoral Advisor:	Ferdinand von Lindemann
Known For:	Azimuthal quantum number, Magnetic quantum number, Group velocity, Momentum operator, Hyperbolic motion in relativity, Tachyonic antitelephone, List of things named after Arnold Sommerfeld
Prizes:	Matteucci Medal (1924) Max-Planck Medal (1931) James Scott Prize Lectureship (1933) Lorentz Medal (1939) Oersted Medal (1949) Fellow of the Royal Society (1926)

Arnold Johannes Wilhelm Sommerfeld, ^[1] (pronounced as /de/; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor and postdoc supervisor to seven Nobel Prize winners and supervised at least 30 other famous physicists and chemists. Only J. J. Thomson's record of mentorship offers a comparable list of high-achieving students.

He introduced the second quantum number, azimuthal quantum number, and the third quantum number, magnetic quantum number.^[2] He also introduced the fine-structure constant and pioneered X-ray wave theory.

Early life and education

Sommerfeld was born in 1868 to 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.^{[3] [4] [5]}

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,^[6] and he also benefited from classes with mathematicians Adolf Hurwitz and David Hilbert and physicist Emil Wiechert.^[7] His participation in the student fraternity Deutsche Burschenschaft resulted in a dueling scar on his face.^[8] He received his Ph.D. on 24 October 1891 (age 22).^[9]

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.^[10] 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.^[11]

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^[12] was completed under Klein, in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen.^[13] 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.^[14]

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^[15] 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 Enzyklopädie der mathematischen Wissenschaften; it was a major undertaking which lasted from 1898 to 1926.

Aachen

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. For his contributions to the understanding of journal bearing lubrication during his time at Aachen, he was named as one of the 23 "Men of Tribology" by Duncan Dowson.^[16]

Munich

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,^[17] 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 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.^[18] 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.^[19] 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.^[20] Four of Sommerfeld's doctoral students,^[21] Werner Heisenberg, Wolfgang Pauli, Peter Debye, and Hans Bethe went on to win Nobel Prizes, while others, most notably, Walter Heitler, Rudolf Peierls,^[22] Karl Bechert, Hermann Brück, Paul Peter Ewald, Eugene Feenberg,^[23] Herbert Fröhlich, Erwin Fues, Ernst Guillemin, Helmut Hönl, Ludwig Hopf, Adolf Kratzer, Otto Laporte, Wilhelm Lenz, Karl Meissner,^[24] Rudolf Seeliger, Ernst C. Stückelberg, Heinrich Welker, Gregor Wentzel, Alfred Landé, and Léon Brillouin^[25] became famous in their own right. Three of Sommerfeld's postdoctoral supervisees, Linus Pauling,^[26] Isidor I. Rabi^[27] and Max von Laue,^[28] won Nobel Prizes, and ten others, William Allis,^[29] Edward Condon,^[30] Carl Eckart,^[31] Edwin C. Kemble,^[32] William V. Houston,^[33] Karl Herzfeld,^[34] Walther Kossel, Philip M. Morse,^{[35] [36]} Howard Robertson,^[37] and Wojciech Rubinowicz^[38] went on to become famous in their own right. Walter Rogowski, an undergraduate student of Sommerfeld at RWTH Aachen, also went on to become famous in his own right. Max Born believed Sommerfeld's abilities included the "discovery and development of talents".^[39] 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.^[40]

While at Munich, Sommerfeld came in contact with the special theory of relativity by Albert Einstein, which was not yet widely accepted. His mathematical contributions to the theory helped its acceptance by the skeptics. In 1914 he worked with Léon Brillouin on the propagation of electromagnetic waves in dispersive media. He became one of the founders of quantum mechanics; some of his contributions included co-discovery of the Sommerfeld–Wilson quantization rules (1915), a generalization of Bohr's atomic model, introduction of the Sommerfeld fine-structure constant (1916), co-discovery with Walther Kossel of the Sommerfeld–Kossel displacement law (1919),^[41] and publishing Atombau und Spektrallinien (1919), which became the "bible"^[42] of atomic theory for the new generation of physicists who developed atomic and quantum physics. The book underwent 4 editions from 1919 to 1924, to incorporate the latest advances in quantum mechanics, before splitting into two volumes.

In 1918, Sommerfeld succeeded Einstein as chair of the Deutsche Physikalische Gesellschaft (DPG). One of his accomplishments was the founding of a new journal.^[43] The scientific papers published in DPG journals became so voluminous, that in 1919 a committee of the DPG 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. 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.^[44]

In the winter semester of 1922/1923, Sommerfeld gave the Carl Schurz Memorial Professor of Physics lectures at the University of Wisconsin–Madison.

In 1927 Sommerfeld applied Fermi–Dirac statistics to the Drude model of electrons in metals – a model put forth by Paul Drude. The new theory solved many of the problems predicting thermal properties the original model had and became known as the Drude–Sommerfeld model.

In 1928/1929, Sommerfeld traveled globally, with major stops in India,^[45] China, Japan, and the United States.

Sommerfeld was a great theoretician. Besides his invaluable contributions to 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 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.^[46]

On 1 April 1935 Sommerfeld achieved emeritus status. He remained 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 German: [[Deutsche Physik]],^{[47] [48]} 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^[49] – 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.^[50] 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".^{[51] [52]}

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."^[53]

Sommerfeld was awarded many honors in his lifetime, such as the Lorentz Medal, the Max-Planck Medal, the Oersted Medal,^{[54] [55]} election to the Royal Society of London, the United States National Academy of Sciences, Academy of Sciences of the USSR, the Indian Academy of Sciences, and other academies including those in Berlin, Munich, Göttingen, and Vienna, as well as having conferred on him numerous honorary degrees from universities including Rostock, Aachen, Calcutta, and Athens. He was nominated for the Nobel Prize 84 times, more than any other physicist (including Otto Stern, who got nominated 82 times^[56]), but he never received the award.^{[57] [58]}

Sommerfeld died on April 26, 1951, in Munich from injuries after a traffic accident while walking with his grandchildren. The accident occurred at the corner of Dietlindenstrasse and Biedersteiner Strasse near his house which was located at Dunantstrasse 6.^{[59] [60]} He is buried at the Nordfriedhof close to where he lived at the time.

In 2004, the center for theoretical physics at the University of Munich was named after him.^[61]

Works

Articles

• Arnold Sommerfeld, "Mathematische Theorie der Diffraction" (The Mathematical Theory of Diffraction), Math. Ann. 47(2–3), pp. 317–374. (1896). .
  • Translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri in Mathematical Theory of Diffraction (Birkhäuser Boston, 2003),
• 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, 315–316 (1949). Address upon receipt of the 1948 Oersted Medal.

Books

See also: Lectures on Theoretical Physics.

• 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)
  • Felix Klein and Arnold Sommerfeld, translated by Raymond J. Nagem and Guido Sandri, The Theory of the Top, vol 1. (Boston: Birkhauser, 2008)

See also

• List of things named after Arnold Sommerfeld

Further reading

• 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., (W. H. Freeman and Company, 1992), (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. , Volume 1: The Torch of Mathematics, 1800 to 1870. University of Chicago Press, paper cover, 1990a.
• 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.
• Kant, Horst, Arnold Sommerfeld – Kommunikation und Schulenbildung in Fuchs-Kittowski, Klaus; Laitko, Hubert; Parthey, Heinrich; Umstätter, Walther (editors), Wissenschaft und Digitale Bibliothek: Wissenschaftsforschung Jahrbuch 1998 135–152 (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),
• Kuhn, Thomas S., John L. Heilbron, Paul Forman, and Lini Allen, Sources for History of Quantum Physics (American Philosophical Society, 1967)
• 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),
• Pauling, Linus, Arnold Sommerfeld: 1868–1951, Science Volume 114, Number 2963, pp. 383–384 (1951)
• Singh, Rajinder, "Arnold Sommerfeld – The Supporter of Indian Physics in Germany" Current Science 81 No. 11, 10 December 2001, pp. 1489–1494
• Walker, Mark, Nazi Science: Myth, Truth, and the German Atomic Bomb (Persius, 1995),

External links

• Annotated bibliography for Arnold Sommerfeld from the Alsos Digital Library for Nuclear Issues
• Arnold Sommerfeld Biography – American Philosophical Society (includes information on his students.)
• Arnold Sommerfeld Biography – Zurich ETH-Bibliothek
• Karin Reich (1995) Die Rolle Arnold Sommerfeld bei der Diskussion um die Vektorrechnung
• Arnold Sommerfeld's Students – The Mathematics Genealogy Project
• N. Mukunda (2015) Arnold Sommerfeld: Physicist and Teacher Beyond Compare from Indian Academy of Sciences
• Michael Eckert (Video): Sommerfeld's Munich Quantum School – 3rd Conference on the History of Quantum Physics (June 2011)
  • Together with: Presentation, including many historical pictures
• Hans Bethe talking about his time as Sommerfeld's Student on Peoples Archive
  • Relativitätstheorie – Sommerfeld's 1921 introduction to special and general relativity for general audiences (German)
• Sommerfeld-Project – Leibniz-Rechenzentrum der Wissenschaften
  • • A collection of digitized materials related to Sommerfeld's and Linus Pauling's structural chemistry research.
• Arnold Sommerfeld and Condensed Matter Physics, Annual Review of Condensed Matter Physics Vol. 8:31–49

Notes and References

1. Born . Max. Max Born. Arnold Johannes Wilhelm Sommerfeld. 1868–1951 . 10.1098/rsbm.1952.0018 . . 8 . 21 . 274–296. 1952 . 768813. 161998194.
2. Web site: 2024-04-22 . Arnold Sommerfeld Quantum Mechanics, Atomic Theory, Mathematics Britannica . 2024-05-12 . www.britannica.com . en.
3. Web site: Arnold Sommerfeld (1868–1951) – Biography – MacTutor History of Mathematics Archive. O'Connor. Robertson. J.J.. E.F.. 31 October 2022. https://archive.today/20221031001322/https://mathshistory.st-andrews.ac.uk/Biographies/Sommerfeld/. 31 October 2022. live.
4. Web site: Sommerfeld, Arnold (Johannes Wilhelm). Encyclopedia.com. Complete Dictionary of Scientific Biography. 31 October 2022. https://archive.today/20221031003718/https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/sommerfeld-arnold-johannes-wilhelm-0. 31 October 2022. live.
5. Book: Eckert, Michael. 2013. Arnold Sommerfeld: Science, Life and Turbulent Times 1868–1951. Artin. Tom. New York. Springer. 9781461474609. 832272564.
6. 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.
7. Mehra, Volume 1, Part 1, 1982, p. 106.
8. http://turnbull.mcs.st-and.ac.uk/~history/Biographies/Sommerfeld.html Sommerfeld Biography
9. http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=31357 Arnold Sommerfeld
10. http://www.amphilsoc.org/library/guides/ahqp/bios.htm Arnold Sommerfeld Biography
11. Arnold Sommerfeld, translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri Mathematical Theory of Diffraction (Birkhäuser Boston, 2003),
12. The title of Sommerfeld's Habilitation dissertation: Die mathematische Theorie der Beugung
13. http://www.lrz-muenchen.de/~Sommerfeld/WWW/AS_Biogr.html Sommerfeld-Project
14. 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.)
15. A curator was the resident government representative at the university.
16. Dowson. Duncan. 1979-10-01. Men of Tribology: William Bate Hardy (1864–1934) and Arnold Sommerfeld (1868–1951). Journal of Lubrication Technology. en. 101. 4. 393–397. 10.1115/1.3453381. 0022-2305. free.
17. Jungnickel, 1990b, pp. 274, 277–278, and 281–285.
18. Jungnickel, 1990b, pp. 157 – 160, 254 ff., 304 ff., and 384 ff.
19. Cassidy, 1992, p. 104.
20. 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.
    • Postdoctoral: William Allis, Boyd Bartlett, Richard Becker, Edward Condon, Carl Eckart, William V. Houston, Edwin C. Kemble, Philip M. Morse, Karel Niessen, Linus Pauling, Isidor Rabi, Howard Robertson, and Fritz Sauter.
    • Undergraduate at Aachen: Walter Rogowski.
21. http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=31357 Arnold Sommerfeld’s Students
22. Peierls spent 1926–1928 in doctoral studies under Sommerfeld. He then went on to finish his Ph.D. under Wolfgang Pauli, at the University of Leipzig; it was granted in 1929. See: American Philosophical Society Author Catalog: Peierls .
23. Eugene Feenberg did doctoral studies with Sommerfeld and completed his Ph.D. in 1933 under Edwin C. Kemble at Harvard University.
24. 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 Physics 23 (7) 477–478 (1955). The author states that he attended Sommerfeld's lectures, and specifically on optics, in 1912.
25. In 1912–1913, Brillouin did graduate work with Sommerfeld. He went on to earn his Doctor d'État ès Sciences in 1920, at the University of Paris, under Paul Langevin. See: American Philosophical Society Author Catalog: Brillouin .
26. 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: Pauling . See also: Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 315–316 (1949). In the article, Sommerfeld specifically mentions as his (postdoctoral) students the Americans Linus Pauling, Edward U. Condon, and I. I. Rabi.
27. 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 – Biographical . See also: Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 315–316 (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 postdoc with Sommerfeld.
28. Walker, 1995, p. 73. Von Laue completed his Habilitation in 1906.
29. 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.
30. After earning his Ph.D., Condon, in 1926 and 1927, on a National Research Council fellowship, funded by the Rockefeller Foundation, did postgraduate work with Sommerfeld in Munich and Max Born in Göttingen. See: American Institute of Physics: Edward Condon and American Philosophical Society –MOLE: Condon . See also: Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 315–316 (1949). In the article, Sommerfeld specifically mentions as his (postdoctoral) students the Americans Linus Pauling, Edward U. Condon, and I. I. Rabi.
31. 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: Eckart – American Philosophical Society. See also Arnold Sommerfeld, Some Reminiscences of My Teaching Career, American Journal of Physics 17 (5) 315–316 (1949).
32. Edwin C. Kemble went to Munich and Göttingen in 1927–1928 to study and do research with Sommerfeld and Max Born, respectively.
33. 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 Biography – The National Academies Press. See also Arnold Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics 17 (5) 315–316 (1949).
34. Herzfeld worked at the University of Munich with Sommerfeld and Kazimierz Fajans, first as a Privatdozent (from 1919 to 1925) and then as an extraordinary professor (from 1925 to 1926). See: Karl Ferdinand Herzfeld 1892–1978, A biographical memoir by Joseph F. Mulligan, National Academy Press, 2001.
35. Paul Kirkpatrick Address of Recommendation by Professor Paul Kirkpatrick, Chairman of the Committee on Awards, American Journal of Physics 17 (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.
36. Philip M. Morse In at the Beginnings: A Physicists Life (MIT Press, second printing 1978) p. 100.
37. 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.
38. Rubinowicz was at Munich from 1916 to 1918.
39. Jungnickel, 1990b, p. 284, quoting from references given in Footnote 100 on the page.
40. Jungnickel, 1990b, p. 283.
41. Mehra, 1982, Volume 1, Part 1, p. 330.
42. Kragh, 2002, p. 155.
43. Cassidy, 1992, p. 106.
44. Kragh, 2002, pp. 150 and 168.
45. Singh, Rajinder "Arnold Sommerfeld – The Supporter of Indian Physics in Germany" Current Science 81 No. 11, 10 December 2001, pp. 1489–1494
46. Beyerchen, 1977, p. 9, citing the following reference: Max Born Sommerfeld als Begründer einer Schule, Die Naturwissenschaften 16 1036 (1928).
47. Beyerchen, 1977, pp. 150–167.
48. 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 received 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. Supporters of German: [[Deutsche Physik]] and elements in the Reichserziehungsministerium had their own list of candidates and the battle commenced, continuing 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, 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.
49. Beyerchen, 1977, p. 166.
50. Hentschel, 1996, p. 265. Document #85 in Hentschel, 1996, pp. 261–266.
51. Hentschel, 1996, p. 291. Document #93 in Hentschel, 1996, pp. 290–292.
52. Hentschel, 1996, Appendix F; see entries for Carl Ramsauer and Ludwig Parndtl.
53. Web site: MacTutor History of Mathematics archive: Arnold Sommerfeld (1868–1951). 2 December 2019.
54. Paul . Kirkpatrick . Address of Recommendation by Professor Paul Kirkpatrick, Chairman of the Committee on Awards . American Journal of Physics . 17 . 5 . 312–314 . 1949. 1949AmJPh..17..312. . 10.1119/1.1989584 .
55. Arnold . Sommerfeld . Some Reminiscences of My Teaching Career . American Journal of Physics . 17 . 5 . 315–316 . 1949. 1949AmJPh..17..315S . 10.1119/1.1989585 . 122912752 .
56. Web site: Nomination Database. www.nobelprize.org. 4 May 2018. live. https://web.archive.org/web/20161106224218/http://www.nobelprize.org/nomination/archive/show_people.php?id=8779. 6 November 2016.
57. Web site: Nomination Database. www.nobelprize.org. 4 May 2018. live. https://web.archive.org/web/20180212085135/https://www.nobelprize.org/nomination/archive/show_people.php?id=8661. 12 February 2018.
58. News: Crawford. Elisabeth. Nobel population 1901–50: anatomy of a scientific elite. Physics World. November 2001. https://web.archive.org/web/20060203183205/http://physicsweb.org/articles/world/14/11/7. 3 February 2006.
59. Web site: University of Texas Cécile DeWitt-Morette December 21 1922 – May 8, 2017. The History of the University of Texas at Austin Department of Physics. [letter from] Prof. Dr. W. Pauli. 19 February 2019. Just now I had a sad experience: my old teacher Sommerfeld died this week in Munich as a consequence of a street accident in the age of 82.. 20 June 2019. https://web.archive.org/web/20190620190524/https://web2.ph.utexas.edu/utphysicshistory/CecileDeWittMorette.html. dead.
60. Book: Chang, Sooyojng . Academic Genealogy of Physicists . Seoul National University Press . 2005 . 121.
61. Web site: Arnold Sommerfeld Center for Theoretical Physics – Home . 12 February 2007 . dead . https://web.archive.org/web/20070210010948/http://www.theorie.physik.uni-muenchen.de/asc/index.php . 10 February 2007 . – Arnold Sommerfeld Center for Theoretical Physics