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 ca ...

who worked with Niels Bohr 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 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 rel ...

at the University of Leiden, 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 in Göttingen, 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 fig ...

. Because

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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 Niels Bohr. 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. He played a role in the ill-fated BKS theory of 1924-5 BKS theory. Kramers left Denmark in 1926 and returned to the Netherlands. He became a full professor in theoretical physics at Utrecht University, where he supervised Tjalling Koopmans. In 1934 he left Utrecht and succeeded Paul Ehrenfest in Leiden. From 1931 until his death he held also a cross appointment at Delft University of Technology. Kramers was one of the founders of the Mathematisch Centrum in Amsterdam. In 1925, with Werner Heisenberg he developed the Kramers–Heisenberg dispersion formula. He is also credited 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. with introducing in 1948 the concept of renormalization into quantum field theory, 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 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 ca ...

. 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 in 1947 and Hughes Medal 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