Hans Kramers | |
|---|---|
 Hans Kramers in July-August 1928, Ann Arbor | |
| Born | Hendrik Anthony Kramers (1894-12-17)17 December 1894 |
| Died | 24 April 1952(1952-04-24) (aged 57) Oegstgeest, Netherlands |
| Nationality | Dutch |
| Alma mater | Leiden University |
| Known for | Kramers 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–Henneberger frame Kramers–Kronig relations Kramers-Moyal expansion Kramers–Wannier duality Bohr–Kramers–Slater theory Klein–Kramers equation Wentzel–Kramers–Brillouin approximation Chain reaction Thermoacoustics Transfer-matrix method |
| Awards | Lorentz Medal (1947) Hughes Medal (1951) |
| Scientific career | |
| Fields | Physics |
| Doctoral advisor | Niels Bohr Paul Ehrenfest |
| Doctoral students | Dirk ter Haar Nico van Kampen Tjalling Koopmans |
Hendrik Anthony "Hans"Kramers (17 December 1894 – 24 April 1952) was a Dutchphysicist who worked withNiels Bohr to understand how electromagnetic waves interact with matter and made important contributions toquantum mechanics andstatistical physics.
Hans Kramers was born on 17 December 1894 inRotterdam.[1] the son of Hendrik Kramers, a physician, and Jeanne Susanne Breukelman.
In 1912 Hans finished secondary education (HBS) in Rotterdam, and studiedmathematics andphysics at theUniversity 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 inGöttingen, was not reachable because of theFirst World War. BecauseDenmark was neutral in this war, as was the Netherlands, he travelled (by ship, overland was impossible) toCopenhagen, where he visited unannounced the then still relatively unknownNiels 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. underEhrenfest in Leiden, on 8 May 1919.[2]
Kramers enjoyed music, and played cello and piano.
He worked for almost ten years in Bohr's group, becoming an associate professor at theUniversity of Copenhagen. He played a role in the ill-fatedBKS theory of 1924-5. Kramers left Denmark in 1926 and returned to the Netherlands. He became a full professor in theoretical physics atUtrecht University, where he supervisedTjalling Koopmans.
In 1925, withWerner Heisenberg he developed theKramers–Heisenberg dispersion formula, and in 1926 he was one of the authors of theWKB method. He is also credited with introducing in 1948 the concept ofrenormalization intoquantum field theory,[3][4] although his approach wasnonrelativistic.[4] He is also credited for theKramers–Kronig relations withRalph Kronig which are mathematical equations relating real and imaginary parts of complex functions constrained bycausality. 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 forKramers' degeneracy theorem.
In 1934 he left Utrecht and succeededPaul Ehrenfest in Leiden. From 1931 until his death he held also a cross appointment atDelft University of Technology.
Kramers was one of the founders of theMathematisch Centrum in Amsterdam.
On 25 October 1920 he was married to Anna Petersen. They had three daughters and one son.
Kramers became member of theRoyal 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 theAmerican Philosophical Society.[6] Kramers won theLorentz Medal in 1947 andHughes Medal in 1951.
