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Hans Kramers

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Hans Kramers
Hans Kramers in c. 1928
Hendrik Anthony Kramers

(1894-12-17)17 December 1894
Died24 April 1952(1952-04-24) (aged 58)
Oegstgeest, Netherlands
Alma materLeiden University
Known forKramers transition matrix
Kramers theory of reaction rates
Kramers' law
Kramers' opacity law
Kramers' degeneracy theorem
Kramers–Anderson superexchange
Kramers–Gaunt factor
Kramers–Heisenberg formula
Kramers–Kronig relations
Kramers-Moyal expansion
Kramers–Wannier duality
Bohr–Kramers–Slater theory
Klein–Kramers equation
Wentzel–Kramers–Brillouin approximation
Chain reaction
Transfer-matrix method
AwardsLorentz Medal (1947)
Hughes Medal (1951)
Scientific career
Doctoral advisorNiels Bohr
Paul Ehrenfest
Doctoral studentsDirk ter Haar
Nico van Kampen
Tjalling Koopmans

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

Hans Kramers was born on 17 December 1894 in Rotterdam.[1] 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 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. Because Denmark was neutral in this war, as was the Netherlands, he travelled (by ship, overland was impossible) to Copenhagen, 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.[2]

Kramers enjoyed music, and played cello and piano.

Academic career[edit]

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. 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.

Kramers (second row, fourth left) at Fifth Solvay Conference

In 1925, with Werner Heisenberg 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 into quantum field theory,[3][4] although his approach was nonrelativistic.[4] 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 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.


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


Kramers became member of the Royal Netherlands Academy of Arts and Sciences in 1929, he was forced to resign in 1942. He joined the Academy again in 1945.[5] He was an International member of the American Philosophical Society.[6] Kramers won the Lorentz Medal in 1947 and Hughes Medal in 1951.


  1. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X. Archived from the original (PDF) on 2016-03-04. Retrieved 2017-02-25.
  2. ^ Hendrik Antonie Kramers (1919). "Intensiteit van spektraallijnen" (PDF).
  3. ^ Kramers presented his work at the Shelter Island Conference, repeated in 1948 at the Solvay Conference. The latter did not appear in print until the Proceedings of the Solvay Conference, published in 1950 (see Laurie M. Brown (ed.), Renormalization: From Lorentz to Landau (and Beyond), Springer, 2012, p. 53).
  4. ^ a b 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.
  5. ^ "Hans A. Kramers (1894 - 1952)". Royal Netherlands Academy of Arts and Sciences. Retrieved 28 July 2015.
  6. ^ "APS Member History". search.amphilsoc.org. Retrieved 2023-04-20.

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