Arnold Sommerfeld

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Arnold Sommerfeld was a notable German physicist who pioneered quantum physics research. His work on X-ray wave theory and the development of the azimuthal and spin quantum numbers to explain an atom’s unique quantum state were seminal contributions to the area of atomic physics. Sommerfeld was more interested in literature and history as a child and was unsure of his future path. When he mingled with great mathematical minds such as David Hilbert, Adolf Hurwitz, and Ferdinand von Lindemann, he realized his calling and decided to pursue a career in exact sciences. Additionally, this mathematician served a one-year term in the defense forces, and unlike many of his contemporaries, Sommerfeld engaged in voluntary military service on a regular basis for the next eight years. Arnold’s encounter with mathematician Felix Klein initiated life-long professional cooperation, and Klein had a significant influence on the trajectory of Arnold’s career. This brilliant intellect is credited with advising the most Nobel laureates during his three-decade teaching career. Continue reading to learn more about Sommerfeld’s contributions to quantum physics.

Childhood & Adolescence

Arnold Sommerfeld was born on 5 December 1868 in Königsberg, East Prussia, to Cäcile Matthias and Franz Sommerfeld. Franz, a member of an affluent and respected family, was a physician.
Sommerfeld graduated from the ‘Altstädtisches Gymnasium’ in 1875; his classmates included German physicist Wilhelm Wien and German mathematician Hermann Minkowski.

He pursued higher studies at the ‘University of Königsberg’ after finishing his matriculation in 1886. Though his primary interest was mathematics, he also took classes at the University in natural sciences, philosophy, and political economy.

Sommerfeld eventually decided to do research on pure mathematics for his dissertation under the supervision of eminent mathematicians such as Hilbert, Hurwitz, and Lindemann.

His thesis, titled ‘Die willkürlichen Functionen in der mathematischen Physik,’ dealt with Eigen functions and partial differential equations (The arbitrary functions in mathematical physics). This promising young mathematician obtained his degree from the ‘University of Königsberg’ in 1891.

Soon afterwards, he enrolled in training to earn a teaching diploma, and after passing the examinations, he enlisted in the military in 1892. He was assigned to Königsberg with the the reserve regiment’ during his one-year stint in the defense forces.

Arnold Sommerfeld’s Career

Sommerfeld relocated to Gottingen in 1893, since the town had developed into “the center of mathematical development” in Germany due to the presence of numerous great mathematical minds. To supplement his income, this aspiring mathematician obtained a job as an assistant at the ‘Mineralogical Institute.’

Arnold met Felix Klein, a distinguished German mathematician known for his work on complex analysis and non-Euclidean geometry, in Gottingen.

Klein subsequently accepted Sommerfeld as an apprentice, and this young genius followed in the footsteps of the famed mathematician in producing his second book. Partial differential equations were also discussed in the debate on mathematical theory of diffraction.’

This outstanding mathematician continued his work on the mathematical theory of diffraction by conducting his own study and submitting his thesis. His study effort qualified him for the country’s highest academic title, and he was named a ‘Privatdozent’ in 1895. This academic distinction conferred on him qualified him to teach at the university level.

Klein and Sommerfeld began a 13-year mathematical collaboration in 1895-96, which resulted in the four-volume work ‘Die Theorie des Kreisels’. The compilation discussed rotating body theory and its application to geophysics, astronomy, and technology.

Due to financial constraints, he accepted a less profitable position as a mathematics professor at Clausthal’s ‘Mining Academy in October 1987. While the job appealed to his brain, it enabled him to support his family and continue his correspondence with Klein from Clausthal.

The mathematics professor then began teaching mechanics at ‘RWTH Aachen University,’ formerly known as ‘Königliche Technische Hochschule Aachen.’
Sommerfeld, at the request of Felix Klein, collaborated with other mathematicians to edit the fifth book of the ‘Mathematical Encyclopaedia’ (Encyklopädie der mathematischen Wissenschaften).

In 1906, he relocated to Munich, where he was appointed ordinarius professor of physics at the ‘University of Munich.’ Wilhelm Röntgen, then-Director of the Munich Physics Institute, proposed Sommerfeld for the job of director of the University’s new ‘Theoretical Physics Institute.’

This remarkable mind subsequently concentrated on demonstrating the X-ray wave theory, which asserted that X-rays were in fact waves, through the use of crystals for diffraction. He also worked on proving Albert Einstein’s theory of relativity mathematically.

Arnold began work on his most significant contribution to science in the field of quantum theory in 1911. He offered a modification to Bohr’s atomic model in which he stated that electrons orbit the nucleus in elliptical orbits rather than circular orbits as originally envisaged.

In 1915, he contributed to the establishment of the ‘Sommerfeld–Wilson quantization rules,’ and a year later, he discovered the ‘Sommerfeld Fine-structure constant,’ a measure of the strength of electromagnetic interaction between elementary charged particles.

He proposed the concept of the ‘Magnetic Quantum Number’ in 1916 and discovered the ‘Inner Quantum Number’ four years later.
In 1919, the famed quantum physicist teamed with contemporary Walther Kossel to develop the Sommerfeld–Kossel displacement law.

Sommerfeld founded a new publication in 1918, following his appointment as chair of the ‘Deutsche Physikalische Gesellschaft,’ one of the world’s largest organizations of physicists. Two years later, an offshoot of the journal, ‘Zeitschrift für Physik,’ was formed to allow young scientists to submit their findings for publication.

This famous physicist was invited to the ‘University of Wisconsin–Madison during the academic term 1922-23 to offer the ‘Carl Schurz Memorial Professor of Physics lectures.
Sommerfeld then used statistical mechanics to refine the ‘Paul Drude model’ of electrons in metals in 1927, coining the term ‘Drude-Sommerfeld model’ for the redefined version.

On 1 April 1935, the ‘University of Munich’ honored the extraordinary and pioneering physicist by conferring on him the status of emeritus professor.

Between 1943 and 1950, he authored a number of books, including ‘Mechanik – Vorlesungen über theoretische Physik Band 1’, ‘Mechanik der deformierbaren Medien – Vorlesungen über theoretische Physik Band 2’, ‘Elektrodynamik – Vorlesungen über theoretische Physik Band 3’, ‘Optik – Vorlesungen über theoretische

Awards and Accomplishments

Throughout his life, this famous scientist received numerous prizes and honors. He was a renowned member of the ‘Royal Society of London,’ the ‘Indian Academy of Sciences,’ the ‘Russian Academy of Sciences,’ and the ‘United States National Academy of Sciences.’

He had obtained honorary degrees from Athens, Calcutta, Rostock, and Aachen universities.
The eminent physicist was awarded the ‘Max-Planck Medal,’ the ‘Lorentz Medal,’ and the ‘Oersted Medal’ for his remarkable contributions to physics.

Personal History and Legacies

Arnold developed feelings for Johanna Höpfner during his stay in Gottingen, but his financial situation proved to be a hurdle, and he was regarded unfit for Johanna. Thus, Sommerfeld accepted a lucrative position as a mathematics professor in Clausthal. Johanna and Arnold married and were blessed with four children.

On 26 April 1951, while out for a stroll with his grandchildren, the pioneering scientist was killed in a road accident.
This illustrious physicist is the namesake of the University of Munich’s ‘Center of Theoretical Physics.’

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Though he was nominated for the Nobel Prize more times than any other physicist, this illustrious scientist was never a recipient.