Arnold Sommerfeld

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Arnold Sommerfeld in Göttingen in 1897

Arnold Johannes Wilhelm Sommerfeld (born December 5, 1868 in Königsberg , East Prussia , † April 26, 1951 in Munich ) was a German mathematician and theoretical physicist .


as a student in Königsberg in 1889 (in stripes of fraternity Germania Konigsberg )

Sommerfeld, the son of a physician interested in natural sciences, began studying mathematics at the Albertina in Königsberg after graduating from high school in 1886 , one of the first universities at which theoretical physics had been established as an independent subject, with a famous seminar by Franz Ernst Neumann and Carl Gustav Jacobi . His academic teachers included such important scholars as David Hilbert , Ferdinand von Lindemann and Adolf Hurwitz . During his studies, as a member of the Germania Königsberg fraternity (joined in 1887), he played numerous courses . One of these fencing matches left him with a distinctive mark on his forehead. He received his doctorate in Königsberg in 1891 under Lindemann on the arbitrary functions in mathematical physics . In his early days, Sommerfeld was decisively influenced by Emil Wiechert . There was also a good friendship between Sommerfeld and Wiechert later on. The early correspondence between Sommerfeld and Wiechert was published by Wilfried Schröder (Arch. Hist. Ex. Sci, 1984).

In 1893, after his military service, Sommerfeld went to the University of Göttingen , the then center of mathematical science in Germany. There he initially became an assistant at the mineralogical institute, but his main interests remained in mathematics and mathematical physics. In 1894 he became an assistant to the mathematician Felix Klein , who became his scientific role model. Under him he wrote his habilitation thesis Mathematical Theory of Diffraction in 1895 and was then initially a private lecturer in mathematics. With Klein he also wrote a book on the theory of the gyro and was commissioned by this to write various sections on physics in the Encyclopedia of Mathematical Sciences .

Arnold Sommerfeld, Stuttgart 1935

Sommerfeld married Johanna Höpfner (1874–1955) in 1897, the daughter of the literary historian and curator Ernst Höpfner (1836–1915). He was offered a full professorship in mathematics at the Bergakademie Clausthal , and in 1900 the chair for technical mechanics at RWTH Aachen University followed . In 1906 he was given a professorship for theoretical physics at the Ludwig Maximilians University in Munich , where he set up an important center for theoretical physics. Although he received offers to other renowned chairs, he spent the rest of his career here, interrupted by a visiting professorship in the USA ( University of Wisconsin , 1922/23) and by traveling as an academic teacher, which took him to Asia (India, China, Japan) and to the USA (1928/29). In 1935 he retired, but continued to teach until 1940. The reason for this long transition was the question of succession: Sommerfeld favored Werner Heisenberg as his successor, but met resistance from representatives of "German Physics" who ultimately chose their - in Sommerfeld's view worst of all - to choose from standing - enforced candidates: Wilhelm Müller . After the end of the National Socialist dictatorship , Sommerfeld tried again after 1945 to find a successor who would be able to continue the tradition of his school and suggested Werner Heisenberg, Karl Bechert , Hans Bethe and Carl Friedrich von Weizsäcker , but they refused.

Sommerfeld died in 1951 as a result of a traffic accident . His grave is in the north cemetery in Munich.


Sommerfeld bust, Munich, LMU , Theresienstr. 37

Along with Max Planck , Albert Einstein and Niels Bohr, Sommerfeld is one of the researchers who created modern theoretical physics with its cornerstones of quantum physics and relativity theory at the beginning of the 20th century and made it the foundation of physics. He was important both as a researcher and as an academic teacher. His contribution to science was less in the formulation of new, disruptive physical theories than in the application of advanced mathematical methods to physical and technical problems. An important contribution to early quantum physics was the expansion of Bohr's model of the atom , so that it could also be used to explain the fine structure of the spectral lines of hydrogen ( Bohr-Sommerfeld's atomic model ). He introduced the fine structure constant α. He also developed a theory of X-rays , improved the Drude theory of metal electrons by applying quantum mechanics ( Drude-Sommerfeld theory ) and worked out a comprehensive theory of the top together with Felix Klein . Sommerfeld was also one of the first physicists who accepted Albert Einstein's special theory of relativity , applied it and thus helped to enforce it. Furthermore, Sommerfeld dealt with hydrodynamic slide bearings and developed the Sommerfeld number named after him as a measure of the load on a bearing and he dealt with stability problems in hydrodynamics ( Orr-Sommerfeld equations ).

Participants in the first Solvay conference (1911)

Sommerfeld was nominated for the Nobel Prize a total of 81 times (only a few selected people are eligible to nominate, e.g. former Nobel Prize winners) - more often than any other physicist before or after him - but never received it. Even as university lecturers, there were more future Nobel Prize winners among his assistants , doctoral students or students than any previous Nobel Prize winner in physics. The so-called Sommerfeld School of Theoretical Physics had a strong influence on the development of its science (especially quantum theory and its dissemination), both because of the quality of its work and because of the many chairs that were subsequently filled by its representatives in Germany and the USA. With Werner Heisenberg and Wolfgang Pauli two of the key in the formulation of quantum mechanics researchers have his doctorate under Sommerfeld. Other doctoral students from Sommerfeld included a. Peter Debye , Hans Bethe , Paul Sophus Epstein , Walter Heitler , Walter Franz , Ludwig Hopf , Herbert Fröhlich , Paul Peter Ewald , Adolf Kratzer , Karl Bechert , Alfred Landé , Wilhelm Lenz , Otto Laporte , Josef Meixner , Albrecht Unsöld , Gregor Wentzel , Ernst Guillemin , Rudolf Seeliger , Helmut Hönl , Fritz Bopp and Heinrich Welker . Foreign post-doctoral students like Isidor Isaac Rabi and Linus Pauling were at his institute.

Not everyone got along with Sommerfeld's personality. Heisenberg said (very respectfully) about him:

“He was an old-style privy councilor with very determined views on morality, politics, behavior and so on. Pauli used to say of him: 'He looks like an old hussar colonel'. He had the mustache, the personality and decisive views. "

- Werner Heisenberg : Interview from March 9, 1963

An anecdote spread by Edward Teller was known and passed on with a smile : The young American (and later Nobel Prize winner) John Hasbrouck Van Vleck studied at the Munich Institute of Physics. One day Van Vleck was sitting in the library and Sommerfeld walked into the room, whereupon Van Vleck rose from the seat and politely said “Good morning Mr. Sommerfeld!”, But was only greeted by Sommerfeld with an unwilling hum. The next morning the scene was repeated, Van Vleck jumped up and said: "Good morning Professor!", Whereupon Sommerfeld smiled a little but did not reply. On the third day the two met again and Van Vleck greeted Sommerfeld with “Good morning, Doctor!”. Sommerfeld also replied with “Good morning!”. On the fourth day, Sommerfeld entered the library again and was greeted by Van Vleck with "Good morning, Privy Councilor !" Thereupon Sommerfeld leaned over to his student in amazement and said with praise: "But your German is getting better every day!"

Sommerfeld also influenced science as the author of specialist books. His book Atombau und Spectral Lines, first published in 1919, was published in continuously expanded editions in the following years, reflecting the rapid development of atomic physics during this period. For a long time it was one of the most important publications that made theoretical knowledge of young quantum mechanics accessible to experimenters and also played an outstanding role in the training of students.

Honors and Membership

Sommerfeld had been a member of the Bavarian Academy of Sciences since 1908, a corresponding member of the Prussian Academy of Sciences since 1920 and a Fellow of the Royal Society London since 1926 . In 1925 he became a corresponding and in 1929 honorary member of the then Soviet Academy of Sciences . He was awarded the Helmholtz Medal in 1917 by the Prussian Academy of Sciences and the Max Planck Medal in 1931 by the German Physical Society . In 1949 he received the AAPT's Oersted Medal . In 1929 Sommerfeld was elected to the National Academy of Sciences , in 1948 to the American Academy of Arts and Sciences . From 1926 until his death in 1951 he was a member of the casual society in Munich . The Academic-Mathematical Association Munich in the AV accepted Sommerfeld as an honorary member.

The Arnold Sommerfeld Center , the research center for theoretical physics at the Ludwig Maximilians University in Munich, and the Arnold Sommerfeld Prize of the mathematical and natural science class of the Bavarian Academy of Sciences were named after him .

The asteroid (32809) Sommerfeld has had his name since 2002.

In the Munich district of Ramersdorf-Perlach , Clausthal-Zellerfeld , Aachen and Baesweiler streets were named after him.


Albert Einstein on Arnold Sommerfeld:

  • “What I particularly admire about you is that you have created a large number of young talents out of the ground. That is something very strange. You must have a gift to refine and activate the spirits of your listeners. ”- Albert Einstein in a letter of January 14, 1922 to Arnold Sommerfeld


  • Theory of the gyro . 4 volumes (together with Felix Klein), Leipzig 1897–1910
  • Atomic structure and spectral lines . Braunschweig 1919, Harri Deutsch 1978, ISBN 3-87144-484-7 . In 1929 the first edition of the second volume of the wave mechanics supplement appeared . Both volumes were revised several times up to 1960.
  • Lectures on theoretical physics. newly published by Verlag Harri Deutsch, Frankfurt:
    • Volume 1: Mechanics . Leipzig 1943, Harri Deutsch 1994, ISBN 3-87144-374-3 .
    • Volume 2: Mechanics of Deformable Media . Leipzig 1945, Harri Deutsch 1992, ISBN 3-87144-375-1 .
    • Volume 3: Electrodynamics . Wiesbaden 1948, Harri Deutsch 2005, ISBN 3-87144-376-X .
    • Volume 4: Optics . Wiesbaden 1950, Harri Deutsch 1988, ISBN 3-87144-377-8 .
    • Volume 5: Thermodynamics and Statistics . Wiesbaden 1952, Harri Deutsch 1988, ISBN 3-87144-378-6 .
    • Volume 6: Partial differential equations in physics . Leipzig 1945, Harri Deutsch 1992, ISBN 3-87144-379-4 .
  • Michael Eckert, Karl Märker (Ed.): Arnold Sommerfeld. Scientific correspondence , 2 volumes, Deutsches Museum / GNT Verlag, 2000, 2004


  • Michael Eckert : The atomic physicists. A history of theoretical physics using the example of the Sommerfeld School . Vieweg, Braunschweig 1993, ISBN 3-528-06500-1 .
  • Suman Seth: Crafting the Quantum. Arnold Sommerfeld and the Practice of Theory, 1890-1926. MIT Press, 2010.
  • Michael Eckert:  Sommerfeld, Arnold Wilhelm Johannes. In: New German Biography (NDB). Volume 24, Duncker & Humblot, Berlin 2010, ISBN 978-3-428-11205-0 , p. 568 f. ( Digitized version ).
  • Michael Eckert: Arnold Sommerfeld, atomic physicist and cultural messenger, 1868–1951. A biography . Wallstein, Göttingen 2013, ISBN 978-3-8353-1206-7 .
    • English edition: Michael Eckert: Arnold Sommerfeld. Science, Life and Turbulent Times 1869–1951 , Springer Verlag 2013
  • Michael Eckert: Sommerfeld and the beginnings of atomic theory , physics in our time, Volume 26, 1995, pp. 21–28

Web links

Commons : Arnold Sommerfeld  - Collection of images, videos and audio files

Video online:

Books and articles by Sommerfeld online:

Individual evidence

  1. ^ Ernst Elsheimer (ed.): Directory of the old fraternity members according to the status of the winter semester 1927/28. Frankfurt am Main 1928, p. 495.
  2. Arnold Sommerfeld in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. Quote: "At the age of 70 I resigned from my teaching post and received the worst possible successor." In: Arnold Sommerfeld: Gesammelte Schriften. Volume 4, Vieweg Verlag, 1968, p. 679: "Autobiographical sketch".
  4. ^ The grave of Arnold Sommerfeld. In:
  5. ^ IOP - Institute of Physics - December
  6. Arnold Sommerfeld in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  7. Thomas S. Kuhn : Interview with Dr. Werner Heisenberg at the Max Planck Institute, Munich, Germany. Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, February 11, 1963, accessed March 9, 2013 .
  8. 19. A lack of enthusiasm for Sommerfeld , Teller in a video on Web of Stories
  9. ^ Foreign members of the Russian Academy of Sciences since 1724. Arnold Johannes Wilhelm Sommerfeld. Russian Academy of Sciences, accessed September 1, 2015 (Russian).
  10. ^ Members of the American Academy. Listed by election year, 1900-1949 ( PDF ). Retrieved October 11, 2015
  11. ^ Gustav Rohmer: The casual society in Munich 1837–1937 , printed as a manuscript, CH Beck'sche Buchdruckerei, Nördlingen 1937
  12. AVZ (Math. Natw. Sheets). Journal of the Arnstädter Verband Mathematischer u. Scientific connections at German universities in the Deutscher Wissenschafter-Verband, vol. 24 (1930), no. 1, p. 19f.
  13. quoted in David C. Cassidy: Werner Heisenberg : Life and Work. Spektrum Akademischer Verlag, Heidelberg 2001, ISBN 3-8274-1116-5 , p. 132.