Hendrik Anthony "Hans" Kramers (17 December 1894 – 24 April 1952) was a Dutch

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

who worked with

Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...

to understand how electromagnetic waves interact with matter and made important contributions to

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

and

statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

Background and education

Hans Kramers was born on 17 December 1894 in

Rotterdam Rotterdam ( , ; ; ) is the second-largest List of cities in the Netherlands by province, city in the Netherlands after the national capital of Amsterdam. It is in the Provinces of the Netherlands, province of South Holland, part of the North S ...

. the son of Hendrik Kramers, a physician, and Jeanne Susanne Breukelman. In 1912 Hans finished secondary education ( HBS) in Rotterdam, and studied

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

at the

University of Leiden Leiden University (abbreviated as ''LEI''; ) is a public research university in Leiden, Netherlands. Established in 1575 by William, Prince of Orange as a Protestant institution, it holds the distinction of being the oldest university in the Neth ...

, where he obtained a master's degree in 1916. Kramers wanted to obtain foreign experience during his doctoral research, but his first choice of supervisor,

Max Born Max Born (; 11 December 1882 – 5 January 1970) was a German-British theoretical physicist 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 ...

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, was not reachable because of the

First World War World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

. Because

Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...

was neutral in this war, as was the Netherlands, he travelled (by ship, overland was impossible) to

Copenhagen Copenhagen ( ) is the capital and most populous city of Denmark, with a population of 1.4 million in the Urban area of Copenhagen, urban area. The city is situated on the islands of Zealand and Amager, separated from Malmö, Sweden, by the ...

, where he visited unannounced the then still relatively unknown

. Bohr took him on as a Ph.D. candidate and Kramers prepared his dissertation under Bohr's direction. Although Kramers did most of his doctoral research (on intensities of atomic transitions) in Copenhagen, he obtained his formal Ph.D. under Ehrenfest in Leiden, on 8 May 1919. Kramers enjoyed music, and played cello and piano.

Academic career

He worked for almost ten years in Bohr's group, becoming an associate professor at the

University of Copenhagen The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. ...

. He played a role in the ill-fated

BKS theory In the history of quantum mechanics, the Bohr–Kramers–Slater (BKS) theory was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the so-called old quantum theory, in which quantum ...

of 1924-5. Kramers left Denmark in 1926 and returned to the Netherlands. He became a full professor in theoretical physics at

Utrecht University Utrecht University (UU; , formerly ''Rijksuniversiteit Utrecht'') is a public university, public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2023, it had an enrollment of ...

, where he supervised

Tjalling Koopmans Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist. He was the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences for his work on the theory ...

In 1925, with

Werner Heisenberg Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II. He pub ...

he developed the Kramers–Heisenberg dispersion formula, and in 1926 he was one of the authors of the WKB method. He is also credited with introducing in 1948 the concept of

renormalization Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...

into

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

, Jagdish Mehra, Helmut Rechenberg, ''The Conceptual Completion and Extensions of Quantum Mechanics 1932-1941. Epilogue: Aspects of the Further Development of Quantum Theory 1942-1999: Volumes 6, Part 2'', Springer, 2001, p. 1050. although his approach was nonrelativistic. He is also credited for the Kramers–Kronig relations with Ralph Kronig which are mathematical equations relating real and imaginary parts of complex functions constrained by causality. One further refers to a Kramers turnover when the rate of thermally activated barrier crossing as a function of the damping goes through a maximum, thereby undergoing a transition between the energy diffusion and spatial diffusion regimes. He is also known for Kramers' degeneracy theorem. In 1934 he left Utrecht and succeeded

Paul Ehrenfest Paul Ehrenfest (; 18 January 1880 – 25 September 1933) was an Austrian Theoretical physics, theoretical physicist who made major contributions to statistical mechanics and its relation to quantum physics, quantum mechanics, including the theory ...

in Leiden. From 1931 until his death he held also a cross appointment at

Delft University of Technology The Delft University of Technology (TU Delft; ) is the oldest and largest Dutch public university, public Institute of technology, technical university, located in Delft, Netherlands. It specializes in engineering, technology, computing, design, a ...

. Kramers was one of the founders of the Mathematisch Centrum in Amsterdam.

Family

On 25 October 1920 he was married to Anna Petersen. They had three daughters and one son.

Recognition

Kramers became member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...

in 1929, he was forced to resign in 1942. He joined the Academy again in 1945. He was an International member of the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

. Kramers won the

Lorentz Medal Lorentz Medal is a distinction 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. The medal is given for imp ...

in 1947 and

Hughes Medal The Hughes Medal is a silver-gilt medal awarded by the Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. T ...

in 1951.

Notes

References

* * *

External links

* H.B.G. Casimir
''Kramers, Hendrik Anthony (1894–1952)''
in ''Biografisch Woordenboek van Nederland''. (in Dutch) * J.M. Romein

in: ''Jaarboek van de Maatschappij der Nederlandse Letterkunde te Leiden, 1951–1953'', pp. 83–91. (in Dutch)

{{DEFAULTSORT:Kramers, Hans 1894 births 1952 deaths 20th-century Dutch physicists Quantum physicists Academic staff of the Delft University of Technology Leiden University alumni Members of the Royal Netherlands Academy of Arts and Sciences Probability theorists Lorentz Medal winners Scientists from Rotterdam Presidents of the International Union of Pure and Applied Physics Members of the Royal Swedish Academy of Sciences International members of the American Philosophical Society