Ludwig Hopf
Encyclopedia
Ludwig Hopf was a German
theoretical physicist
who made contributions to mathematics
, special relativity
, hydrodynamics, and aerodynamics
.
Hopf studied under Arnold Sommerfeld
at the University of Munich, where he received his Ph.D. in 1909, on the topic of hydrodynamics. Shortly after this, at a physics conference in Salzburg
, Sommerfeld introduced Hopf to Albert Einstein
. Later that year, Einstein, needing an assistant at the University of Zurich
, hired Hopf; it was an added bonus that Hopf was a talented pianist, since Einstein played the violin and liked to play duets. In 1910, he collaborated and published with Einstein two papers on classical statistical aspects of radiation. Hopf’s collaboration with Sommerfeld on integral representations of Bessel Functions resulted in the publication of a paper in 1911. Also in that year, Hopf accompanied Einstein to the Karl-Ferdinand University in Prague
; however, he did not stay with Einstein long – due to “unsanitary conditions” in Prague. He accepted a position at the Aachen
Technische Hochschule
, where he eventually became a professor in hydrodynamics and aerodynamics
. During World War I
, he contributed to the design of military aircraft. It was during his tenure at Aachen that he made a contribution to the Handbuch der Physik and co-authored a “highly esteemed” book on aerodynamics. In 1934, due to his being “non-Aryan”, he lost his position at Aachen; he moved to Dublin, Ireland
and became a professor of mathematics at Trinity College
. One of his colleagues there was the Austrian physicist Erwin Schrödinger
.
In 1939, Hopf became seriously ill in December and died on December 21.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
theoretical physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
who made contributions to mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, hydrodynamics, and aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
.
Hopf studied under Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
at the University of Munich, where he received his Ph.D. in 1909, on the topic of hydrodynamics. Shortly after this, at a physics conference in Salzburg
Salzburg
-Population development:In 1935, the population significantly increased when Salzburg absorbed adjacent municipalities. After World War II, numerous refugees found a new home in the city. New residential space was created for American soldiers of the postwar Occupation, and could be used for...
, Sommerfeld introduced Hopf to 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...
. Later that year, Einstein, needing an assistant at the University of Zurich
University of Zurich
The University of Zurich , located in the city of Zurich, is the largest university in Switzerland, with over 25,000 students. It was founded in 1833 from the existing colleges of theology, law, medicine and a new faculty of philosophy....
, hired Hopf; it was an added bonus that Hopf was a talented pianist, since Einstein played the violin and liked to play duets. In 1910, he collaborated and published with Einstein two papers on classical statistical aspects of radiation. Hopf’s collaboration with Sommerfeld on integral representations of Bessel Functions resulted in the publication of a paper in 1911. Also in that year, Hopf accompanied Einstein to the Karl-Ferdinand University in Prague
Prague
Prague is the capital and largest city of the Czech Republic. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of over 2.3 million...
; however, he did not stay with Einstein long – due to “unsanitary conditions” in Prague. He accepted a position at the Aachen
Aachen
Aachen has historically been a spa town in North Rhine-Westphalia, Germany. Aachen was a favoured residence of Charlemagne, and the place of coronation of the Kings of Germany. Geographically, Aachen is the westernmost town of Germany, located along its borders with Belgium and the Netherlands, ...
Technische Hochschule
Technische Hochschule
Technische Hochschule is what an Institute of Technology used to be called in German-speaking countries, as well as in the Netherlands, before most of them changed their name to Technische Universität or Technische Universiteit in the 1970s and in the...
, where he eventually became a professor in hydrodynamics and aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
. During World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, he contributed to the design of military aircraft. It was during his tenure at Aachen that he made a contribution to the Handbuch der Physik and co-authored a “highly esteemed” book on aerodynamics. In 1934, due to his being “non-Aryan”, he lost his position at Aachen; he moved to Dublin, Ireland
Ireland
Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...
and became a professor of mathematics at Trinity College
Trinity College, Dublin
Trinity College, Dublin , formally known as the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by letters patent from Queen Elizabeth I as the "mother of a university", Extracts from Letters Patent of Elizabeth I, 1592: "...we...found and...
. One of his colleagues there was the Austrian physicist Erwin Schrödinger
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...
.
In 1939, Hopf became seriously ill in December and died on December 21.
Books
- Ludwig Hopf, Introduction to the Differential Equations of Physics. Translated by Walter Nef. New York: Dover Publications, 1948.
See also
- Einstein - Hopf DragEinstein - Hopf DragIn physics, the Einstein–Hopf drag is a velocity-dependent drag force upon charged particles that are being bathed in thermal radiation....