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 caus ...

who worked with

Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. B ...

to understand how electromagnetic waves interact with matter and made important contributions to quantum mechanics and statistical physics.

Background and education

Hans Kramers was born on 17 December 1894 in

Rotterdam Rotterdam ( , , , lit. ''The Dam on the River Rotte'') is the second largest city and municipality in the Netherlands. It is in the province of South Holland, part of the North Sea mouth of the Rhine–Meuse–Scheldt delta, via the ''"N ...

. 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 an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

physics Physics is the natural science that studies matter, its 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 which r ...

at the

University of Leiden Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...

, 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 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 n ...

Göttingen Göttingen (, , ; nds, Chöttingen) 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. At the end of 2019, t ...

, was not reachable because of the

First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

. Because

Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Danish Realm, Kingdom of Denmark ...

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

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

, 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 Ehrenfest is a surname. Notable people with the surname include: *Paul Ehrenfest (1880-1933), Austrian physicist and mathematician **Ehrenfest equations **Ehrenfest model **Ehrenfest paradox **Ehrenfest theorem The Ehrenfest theorem, named after P ...

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 ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

. He played a role in the ill-fated BKS theory of 1924-5

BKS theory The Bohr–Kramers–Slater theory (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 phenomena are treated by imposi ...

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

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

, 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 1934 he left Utrecht and succeeded

Paul Ehrenfest Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition a ...

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

Delft University of Technology Delft University of Technology ( nl, Technische Universiteit Delft), also known as TU Delft, is the oldest and largest Dutch public technical university, located in Delft, Netherlands. As of 2022 it is ranked by QS World University Rankings among ...

. Kramers was one of the founders of the

Mathematisch Centrum The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Cou ...

in Amsterdam. In 1925, with

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...

he developed the Kramers–Heisenberg dispersion formula. He is also credited

Jagdish Mehra Jagdish Mehra (April 8, 1931 – September 14, 2008) was an Indian-American historian of science. Academic career Mehra was educated at Allahabad University, the Max Planck Institut für Physik and the University of California at Los Angeles a ...

Helmut Rechenberg Helmut Rechenberg (born November 6, 1937, in Berlin; died November 10, 2016, in Munich) was a German physicist and science historian. Rechenberg studied mathematics, physics and astronomy at the University of Munich and graduated in 1964. At Mun ...

, ''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. with introducing in 1948 the concept of

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

into

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

, although his approach was

nonrelativistic The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

. He is also credited for the

Kramers–Kronig relations The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane. The relations are often used to compute the real part from the imag ...

with

Ralph Kronig Ralph Kronig (10 March 1904 – 16 November 1995) was a German physicist. He is noted for the discovery of particle spin and for his theory of X-ray absorption spectroscopy. His theories include the Kronig–Penney model, the Coster–Kronig tran ...

which are mathematical equations relating real and imaginary parts of complex functions constrained by

causality Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...

. 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%27_theorem.

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 ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

in 1929, he was forced to resign in 1942. He joined the Academy again in 1945. 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 impor ...

in 1947 and

Hughes Medal The Hughes Medal is awarded by the Royal Society of London "in recognition of an original discovery in the physical sciences, particularly electricity and magnetism or their applications". Named after David E. Hughes, the medal is awarded with ...

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 Delft University of Technology faculty 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