Arnold Sommerfeld

Arnold Sommerfeld

Overview
Arnold Johannes Wilhelm Sommerfeld (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

 and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics. He was nominated a record 81 times for the Nobel Prize, and served as PhD supervisor for more Nobel prize winners in physics than any other supervisor before or since.
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Encyclopedia
Arnold Johannes Wilhelm Sommerfeld (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

 and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics. He was nominated a record 81 times for the Nobel Prize, and served as PhD supervisor for more Nobel prize winners in physics than any other supervisor before or since. He introduced the 2nd quantum number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant
Fine-structure constant
In physics, the fine-structure constant is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units...

, and pioneered X-ray wave theory.

Education


Sommerfeld studied mathematics and physical sciences at the Albertina University
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....

 of his native city, Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...

, East Prussia
East Prussia
East Prussia is the main part of the region of Prussia along the southeastern Baltic Coast from the 13th century to the end of World War II in May 1945. From 1772–1829 and 1878–1945, the Province of East Prussia was part of the German state of Prussia. The capital city was Königsberg.East Prussia...

. His dissertation advisor was the mathematician Ferdinand von Lindemann
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i.e., it is not a root of any polynomial with rational coefficients....

, and he also benefited from classes with mathematicians Adolph Hurwitz and David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...

, and physicist Emil Wiechert
Emil Wiechert
Emil Johann Wiechert was a German geophysicist who presented the first verifiable model of a layered structure of the Earth.-Life:...

. His participation in the student fraternity Deutsche Burschenschaft
Burschenschaft
German Burschenschaften are a special type of Studentenverbindungen . Burschenschaften were founded in the 19th century as associations of university students inspired by liberal and nationalistic ideas.-History:-Beginnings 1815–c...

 resulted in a fencing scar on his face. He received his Ph.D. in 1891 (age 23).

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 Prussia
Prussia
Prussia was a German kingdom and historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organized and effective army. Prussia shaped the history...

n bearing, and the fencing scar on his face, he gave the impression of being a colonel in the hussar
Hussar
Hussar refers to a number of types of light cavalry which originated in Hungary in the 14th century, tracing its roots from Serbian medieval cavalry tradition, brought to Hungary in the course of the Serb migrations, which began in the late 14th century....

s.

Göttingen


In October, 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
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...

'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 Habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...

sschrift was completed under Klein, in 1895, which allowed Sommerfeld to become a Privatdozent
Privatdozent
Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...

 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
Clausthal-Zellerfeld
Clausthal-Zellerfeld is a town in Lower Saxony, Germany. It is located in the southwestern part of the Harz mountains. Its population is approximately 15,000, Clausthal-Zellerfeld is also the seat of the Samtgemeinde Oberharz....

; he was successor to Wilhelm Wien
Wilhelm Wien
Wilhelm Carl Werner Otto Fritz Franz Wien was a German physicist who, in 1893, used theories about heat and electromagnetism to deduce Wien's displacement law, which calculates the emission of a blackbody at any temperature from the emission at any one reference temperature.He also formulated an...

. This appointment provided enough income to eventually marry Johanna.

At Klein's request, Sommerfeld took on the position of editor of Volume V of Encyklopädie der mathematischen Wissenschaften
Klein's encyclopedia
In mathematics, Klein’s encyclopedia refers to a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Meyer were organizers of the encyclopedia. Its title in English is "Encyclopedia of mathematical sciences including their applications", which is...

; 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
Ludwig Hopf
Ludwig Hopf was a German theoretical physicist who made contributions to mathematics, special relativity, hydrodynamics, and aerodynamics....

 and Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

 would write their Ph.D. theses on this topic.

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, 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
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

 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
Wolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

, Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

, and Walter Heitler
Walter Heitler
Walter Heinrich Heitler was a German physicist who made contributions to quantum electrodynamics and quantum field theory...

 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.

For a list of students, please see the list organized by type. Four of Sommerfeld's doctoral students, Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

, Wolfgang Pauli
Wolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

, Peter Debye
Peter Debye
Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

, and Hans Bethe
Hans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...

 went on to win Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

s, while others, most notably, Walter Heitler
Walter Heitler
Walter Heinrich Heitler was a German physicist who made contributions to quantum electrodynamics and quantum field theory...

, Rudolf Peierls
Rudolf Peierls
Sir Rudolf Ernst Peierls, CBE was a German-born British physicist. Rudolf Peierls had a major role in Britain's nuclear program, but he also had a role in many modern sciences...

, Karl Bechert
Karl Bechert
Karl Richard Bechert was a German theoretical physicist and political leader. As a scientist, his contributions were in atomic physics.-Scientific career:...

, Hermann Brück
Hermann Brück
Hermann Alexander Brück was a German-born astronomer who spent the great portion of his career in the United Kingdom.-Education:...

, Paul Peter Ewald
Paul Peter Ewald
Paul Peter Ewald was a German-born U.S. crystallographer and physicist, a pioneer of X-ray diffraction methods.-Education:...

, Eugene Feenberg
Eugene Feenberg
Eugene Feenberg was an American physicist who made contributions to quantum mechanics and nuclear physics.-Education:...

, Herbert Fröhlich
Herbert Fröhlich
Herbert Fröhlich was a German-born British physicist and a Fellow of the Royal Society....

, Erwin Fues
Erwin Fues
Erwin Richard Fues was a German theoretical physicist who made contributions to atomic physics and molecular physics, quantum wave mechanics, and solid-state physics.-Education and career:...

, Ernst Guillemin
Ernst Guillemin
Ernst Adolph Guillemin was an American electrical engineer and computer scientist at the Massachusetts Institute of Technology who spent his career extending the art and science of linear network analysis and synthesis.-Biography:Guillemin was born in 1898, in Milwaukee, and received his B.S. and...

, Helmut Hönl
Helmut Hönl
Helmut Hönl was a German theoretical physicist who made contributions to quantum mechanics and the understanding of atomic and molecular structure....

, Ludwig Hopf
Ludwig Hopf
Ludwig Hopf was a German theoretical physicist who made contributions to mathematics, special relativity, hydrodynamics, and aerodynamics....

, Adolf Kratzer
Adolf Kratzer
B. Adolf Kratzer was a German theoretical physicist who made contributions to atomic physics and molecular physics, and was an authority on molecular band spectroscopy...

, Otto Laporte
Otto Laporte
Otto Laporte was a German-born American physicist who made contributions to quantum mechanics, electromagnetic wave propagation theory, spectroscopy, and fluid dynamics...

, Wilhelm Lenz
Wilhelm Lenz
Wilhelm Lenz was a German physicist, most notable for his invention of the Ising model and for his application of the Laplace–Runge–Lenz vector to the quantum mechanical treatment of hydrogen-like atoms.In 1906, Lenz graduated from the Klinger-Oberralschule, a non-classical secondary school...

, Karl Meissner
Karl Meissner
Karl Wilhelm Meissner was a German-American physicist specializing in hyperfine spectroscopy...

, Rudolf Seeliger
Rudolf Seeliger
Rudolf Seeliger was a German physicist who specialized in electric discharges in gases and plasma physics....

, Ernst C. Stückelberg, Heinrich Welker
Heinrich Welker
Heinrich Johann Welker was a German theoretical and applied physicist who invented the "transistron", a form of transistor made at Westinghouse independently of the first successful transistor made at Bell Laboratories...

, Gregor Wentzel
Gregor Wentzel
Gregor Wentzel was a German physicist known for development of quantum mechanics. Wentzel, Hendrik Kramers, and Léon Brillouin developed the Wentzel–Kramers–Brillouin approximation in 1926...

, Alfred Landé
Alfred Landé
Alfred Landé was a German-American physicist known for his contributions to quantum theory. He is responsible for the Landé g-factor an explanation of the Zeeman Effect.-Life and Achievements:...

, and Léon Brillouin
Léon Brillouin
Léon Nicolas Brillouin was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory.-Early life:...

 became famous in their own right. Three of Sommerfeld's postgraduate students, Linus Pauling
Linus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...

, Isidor I. Rabi and Max von Laue
Max von Laue
Max Theodor Felix von Laue was a German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals...

 , won Nobel Prizes, and ten others, William Allis
William Allis
William Phelps Allis was an American theoretical physicist specializing in electrical discharges in gases. He was the grandson of Edward P. Allis, a co-founder of Allis-Chalmers.-Education:Allis majored in school and received his S.B. in 1923 and S.M...

, Edward Condon
Edward Condon
Edward Uhler Condon was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II.-Early life and career:...

, Carl Eckart
Carl Eckart
Carl Henry Eckart was an American physicist, physical oceanographer, geophysicist, and administrator. He co-developed the Wigner-Eckart theorem and is also known for the Eckart conditions in quantum mechanics.-Education:Eckart began college in 1919 at Washington University in St...

, Edwin C. Kemble
Edwin C. Kemble
Edwin Crawford Kemble was an American physicist who made contributions to the theory of quantum mechanics and molecular structure and spectroscopy...

, William V. Houston, Karl Herzfeld
Karl Herzfeld
Karl Ferdinand Herzfeld was an Austrian-American physicist.-Education:...

, Walther Kossel
Walther Kossel
Walther Ludwig Julius Kossel was a German physicist known for his theory of the chemical bond , Sommerfeld–Kossel displacement law of atomic spectra, the Kossel-Stranski model for crystal growth, and the Kossel effect...

, Philip M. Morse
Philip M. Morse
Philip McCord Morse , was an American physicist, administrator and pioneer of operations research in World War II. He is considered to be the father of operations research in the U.S.- Biography :Morse graduated from the Case School of Applied Science in 1926 with a B.S. in physics. He earned his...

, Howard Robertson
Howard Percy Robertson
Howard Percy Robertson was an American mathematician and physicist known for contributions related to physical cosmology and the uncertainty principle...

, and Wojciech Rubinowicz
Wojciech Rubinowicz
Wojciech Sylwester Piotr Rubinowicz was a Polish theoretical physicist who made contributions in quantum mechanics, mathematical physics, and the theory of radiation...

 went on to become famous in their own right. Walter Rogowski
Walter Rogowski
Walter Rogowski was a German physicist who bridged the gap between theoretical physics and applied technology in numerous areas of electronics; the Rogowski coil was named after him....

, an undergraduate student of Sommerfeld at RWTH Aachen
RWTH Aachen
RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....

, also went on to become famous in his own right. Max Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

 believed Sommerfeld's abilities included the "discovery and development of talents." Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 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.

While at Munich, Sommerfeld came in contact with the special theory of relativity by Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

, which was not yet widely accepted at that time. His mathematical contributions to the theory helped its acceptance by the skeptics. In 1914 he worked with Léon Brillouin
Léon Brillouin
Léon Nicolas Brillouin was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory.-Early life:...

 on the propagation of electromagnetic waves in dispersive media. He became one of the founders of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

; some of his contributions included co-discovery of the Sommerfeld–Wilson quantization rules (1915), a generalization
Old quantum theory
The old quantum theory was a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics...

 of Bohr's atomic model
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...

, introduction of the Sommerfeld fine-structure constant
Fine-structure constant
In physics, the fine-structure constant is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction. Being a dimensionless quantity, it has constant numerical value in all systems of units...

 (1916), co-discovery with Walther Kossel
Walther Kossel
Walther Ludwig Julius Kossel was a German physicist known for his theory of the chemical bond , Sommerfeld–Kossel displacement law of atomic spectra, the Kossel-Stranski model for crystal growth, and the Kossel effect...

 of the Sommerfeld–Kossel displacement law (1919), and published Atombau und Spektrallinien (1919), which became the "bible" of atomic theory for the new generation of physicists who developed atomic and quantum physics.

In 1918, Sommerfeld succeeded Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 as chair of the Deutsche Physikalische Gesellschaft
Deutsche Physikalische Gesellschaft
The Deutsche Physikalische Gesellschaft is the world's largest organization of physicists. The DPG's worldwide membership is cited as 60,000, as of 2011...

 (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
Zeitschrift für Physik
The European Physical Journal is a joint publication of EDP Sciences, Springer Science+Business Media, and the Società Italiana di Fisica...

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 the winter semester of 1922/1923, Sommerfeld gave the Carl Schurz Memorial Professor of Physics lectures at the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...

.

In 1927 Sommerfeld applied Fermi–Dirac statistics to the Drude model
Drude model
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials...

 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 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
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...

 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.
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
Reichserziehungsministerium
The Reichserziehungsministerium was officially known as the Reichsministerium für Wissenschaft, Erziehung und Volksbildung .-Background:...

 (Acronym: REM, and translation: Reich Education Ministry.) and the supporters of Deutsche Physik
Deutsche Physik
Deutsche Physik or Aryan Physics was a nationalist movement in the German physics community in the early 1930s against the work of Albert Einstein, labeled "Jewish Physics"...

, which was anti-Semitic and had a bias against theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, especially including quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. 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
Deutsche Physikalische Gesellschaft
The Deutsche Physikalische Gesellschaft is the world's largest organization of physicists. The DPG's worldwide membership is cited as 60,000, as of 2011...

 – 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
Kaiser Wilhelm Institute
The Kaiser Wilhelm Society for the Advancement of Science was a German scientific institution established in 1911. It was implicated in Nazi science, and after the Second World War was wound up and its functions replaced by the Max Planck Society...

), and Carl Ramsauer, director of the research division of the Allgemeine Elektrizitäts-Gesellschaft
AEG
Allgemeine Elektricitäts-Gesellschaft was a German producer of electrical equipment founded in 1883 by Emil Rathenau....

 (General Electric Company) and president of the Deutsche Physikalische Gesellschaft
Deutsche Physikalische Gesellschaft
The Deutsche Physikalische Gesellschaft is the world's largest organization of physicists. The DPG's worldwide membership is cited as 60,000, as of 2011...

, 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
Hermann Göring
Hermann Wilhelm Göring, was a German politician, military leader, and a leading member of the Nazi Party. He was a veteran of World War I as an ace fighter pilot, and a recipient of the coveted Pour le Mérite, also known as "The Blue Max"...

, 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
Bernhard Rust
Dr. Bernhard Rust was Minister of Science, Education and National Culture in Nazi Germany. A combination of school administrator and zealous Nazi, he issued decrees, often bizarre, at every level of the German educational system to immerse German youth in the National Socialist philosophy...

, Ramsauer concluded that the appointment amounted to the "destruction of the Munich theoretical physics tradition."

Sommerfeld was awarded many honors in his lifetime, such as the Lorentz Medal
Lorentz Medal
Lorentz Medal is a prize awarded every four years by the Royal Netherlands Academy of Arts and Sciences. It was established in 1925 on the occasion of the 50th anniversary of the doctorate of Hendrik Lorentz. This solid gold medal is given for important contributions to theoretical physics, though...

, the Max-Planck Medal, the Oersted Medal
Oersted Medal
The Oersted Medal recognizes notable contributions to the teaching of physics. Established in 1936, it is awarded by the American Association of Physics Teachers. The award is named for Hans Christian Ørsted. It is the Association's most prestigious award....

, election to the Royal Society of London, the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...

, Academy of Sciences of the USSR, the Indian Academy of Sciences
Indian Academy of Sciences
The Indian Academy of Sciences, Bangalore was founded by Sir C. V. Raman, and was registered as a Society on 24 April 1934. Inaugurated on 31 July 1934, it began with 65 founding fellows. The first general meeting of Fellows, held on the same day, elected Professor Raman as President, and adopted...

, 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.

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

Though Sommerfeld was nominated for the Nobel Prize 81 times, more than any other physicist, he never received the award.

Sommerfeld died in 1951 in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...

 from injuries after a traffic accident while walking with his grandchildren.

Selected literature

  • A. 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

  • Arnold Sommerfeld "Mathematische Theorie der Diffraction" Math. Ann. 47 317–374 (1896)
    • Arnold Sommerfeld, translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri Mathematical Theory of Diffraction (Birkhäuser Boston, 2003) ISBN 0-8176-3604-8
  • 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
    Friedrich Bopp
    Friedrich Arnold Bopp was a German theoretical physicist who contributed to nuclear physics and quantum field theory. He worked at the Kaiser-Wilhelm Institut für Physik and with the Uranverein. He was a professor at the Ludwig Maximilian University of Munich and a President of the Deutsche...

     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, 1964)
  • Felix Klein
    Felix Klein
    Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...

     and Arnold Sommerfeld Über die Theorie des Kreisels [4 volumes] (Teubner, 1897)

See also

  • Bohr–Sommerfeld quantization
  • Grimm-Sommerfeld rule
    Grimm-Sommerfeld rule
    In chemistry, the Grimm-Sommerfeld rule applies for the bond lengths: If the sum of the atomic number is the same, the interatomic distances are the same.-References:...

  • Orr–Sommerfeld equation
  • Quantum mechanics
    Quantum mechanics
    Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

  • Sommerfeld number
    Sommerfeld number
    In the design of fluid bearings, the Sommerfeld number, or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic lubrication analysis...


External links