Arnold Sommerfeld


Arnold Sommerfeld is one of the pioneers of quantum and atomic physics. He was a German theoretical physicist who not only paved way for the development of certain concepts, but also educated and helped a great many students for the then upcoming era of new theoretical physics. It can be said that back then, he was one of the few who thoroughly understood the subject well enough to teach others about it. Interestingly, he had been the mentor for more Nobel Prize recipients in physics compared to any other person before and to this day, he still holds that record. He is more popularly known for introducing the azimuthal quantum number or the 2nd quantum number and the spin quantum number or the 4th quantum number. Along with those achievements, he also pioneered the X-ray wave theory and introduced what is now known as the fine-structure consonant.

Early Life and Educational Background

He was born on the 5th of December in 1868 in Konigsberg located in the Province of East Prussia. He attended high school from 1875-1886 at Altstädtisches Gymnasium, Königsberg and was educated in mathematics as well as physics at Konigsberg’s Albertina University. For his dissertation, he was under his advisor Ferdinand von Lindemann, who was a renowned mathematician. Apart from being taught by Ferdinand von Lindemann, he also had exposure to lectures given by the mathematicians David Hilbert and Adolf Hurwitz, and Emil Wiechert, a known physicist. He was 23 when he received his Ph.D.


After receiving his doctorate, Sommerfeld concentrated on the academe. He worked on his teaching diploma and was able to pass the national exam in 1892. After that, he served for a year in the military and completed the obligatory service in 1893. He still continued with the voluntary 8-week service for eight more years.

Sommerfeld proceeded to the University of Göttingen where he became the teaching assistant of Theodore Liebsich, who was working at the Mineralogical Institute. Liebsich was one of the professors at the University of Göttingen and also happened to be a family friend of the Sommerfelds. In 1894, Sommerfeld was given the chance to be Felix Klein’s assistant. Klein was a German mathematician known for his works on non-Euclidean geometry and complex analysis, among others. During Sommerfeld’s time with Klein he had to take notes of the lectures and managed the Mathematics Reading Room as well. Sommerfeld’s dissertation called “Habilitationsschrift” was completed while he was working under Klein and achieved completion in 1895. This dissertation allowed him to be one of the Privatdozents of Gottingen.

When he was a Privatdozent already, Sommerfeld himself lectured on a wide range of subjects including mathematical as well as physics lessons. Lectures given about partial differential equations were first available in the Gottingen and over his course as a teacher, he was able to compile the textbooks series called Lectures on Theoretical Physics and the partial differential equations in particular were present in Volume VI. Together with Klein, they wrote the 4-volume Die Theorie des Kreisels which was about rotating bodies. This compilation took 13 years to complete, from 1897 to 1910.

It was in 1900 when Sommerfeld became the Chair of Applied Mechanics which he held at the Königliche Technische Hochschule Aachen, as one of its extraordinarius professors. This was made possible through Klein himself. During Sommerfeld’s time in Aachen, he was able to develop the theory concerned about hydrodynamics—something that was able to retain his interest even after years from his initial exposure to it.

In 1906, Sommerfeld went to the University of Munich where he became as an ordinarius professor of physics as well as be the Theoretical Physics Institute director. It was none other than Wilhelm Rontgen himself who selected these positions to be held by Sommerfeld. These positions were held with Sommerfeld’s highest regards, and in his words, it was something much like being asked to participated in a “privileged sphere of action.”

He spent over 32 years in Munich, teaching general as well as special courses. His topics ranged from the mechanics that deformable bodies had, optics, electrodynamics, thermodynamics, mechanics, partial differential equations in physics, and even statistical mechanics. He held these lectures for four hours a week for 13 weeks during the winter and 11 weeks during the summer.

Also during his time in Munich, he came into contact with Albert Einstein’s special theory of relativity. Back then, this theory was not yet widely accepted, and it was because of the mathematical contributions that Arnold Sommerfeld made that this theory was accepted by skeptics. He had also been one of the main proponents of quantum mechanics. Some of his contributions include the Sommerfeld–Wilson quantization rules discovered in 1915, and the Sommerfeld fine-structure constant which was discovered a year later.

In 1918, he was Albert Einstein’s successor as the chairperson of the DGP or the Deutsche Physikalische Gesellschaft, and one of the accomplishments he had was to establish a new journal which led to the establishment of the Zeitschrift für Physik, where the original research articles were published.

In 1928-1929, he travelled the world and was able to visit India, Japan, China, and the United States as well. He was known as a great theoretician and apart from his irreplaceable and timeless works in physics, he also had other contributions in other fields—most notably on the classical theory of electromagnetism.

He received the emeritus status on the first of April in 1935 but stayed on as his own replacement while his successor was still being selected. The selection process took four long years and it was not until the first of December when his replacement had been recognized.

He was the recipient of several medals like the Max-Planck Medal, Lorentz Medal, and several more acknowledgments from universities all over the world. He has been nominated for the Nobel Prize 81 times, but never received an award of his own. He died in an automobile accident in Munich on the 25th of April in 1951.