Background

Hans Kramers was born on December 17, 1894, in Rotterdam, Netherlands. He was the third of five sons of Hendrik Kramers, a physician, and Jeanne Susanne Breukelman.

Education

Kramers received his early schooling at Rotterdam. In 1912 he went to Leiden and studied theoretical physics, mainly with P. Ehrenfest, who in 1912 had succeeded H. A. Lorentz. In 1916 he obtained his master’s degree.

Kramers wanted to obtain foreign experience during his doctoral research, but his first choice of supervisor, Max Born in Gottingen, was not reachable because of the first world war. Because Denmark was neutral in this war, as was the Netherlands, he traveled 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 May 8, 1919.

Career

In 1916 Kramers taught for a few months in a secondary school and in September set out for Copenhagen, where he became a close collaborator of Niels Bohr. In 1920 Bohr’s Institute of Theoretical Physics was opened; Kramers was first an assistant and in 1924 became a lecturer. In 1926 he accepted the chair of theoretical physics at Utrecht and in 1934 returned to Leiden as a successor to Ehrenfest, who had died in September 1933. From 1934 until his death Kramers taught at Leiden and paid numerous visits to other countries, including the United States.

In 1946 Kramers was elected chairman of the Scientific and Technological Committee of the United Nations Atomic Energy Commission, and he presented a unanimous report on the technological feasibility of control of atomic energy. From 1946 to 1950 he was president of the International Union of Pure and Applied Physics.

Achievements

• Hans Kramers went down in history as a distinguished physicist and university professor. With Ralph de Laer Kronig, he derived important equations relating the absorption to the dispersion of light. He also predicted the existence of the Raman effect, inelastic scattering of light, and showed that the complex form of the mathematical functions in dispersion theory, concerning collisions of subatomic particles, results from the inability of a signal to be propagated faster than the speed of light. His research on X rays resulted in his development of equations to determine the efficiency and intensity of X-ray production.
  
  His work, which covers almost the entire field of theoretical physics, is characterized both by outstanding mathematical skill and by careful analysis of physical principles. It also leaves us with the impression that he tackled problems because he found them challenging, not primarily because they afforded chances of easy success. As a consequence his work is somewhat lacking in spectacular results that can easily be explained to a layman; but among fellow theoreticians, he was universally recognized as one of the great masters. He played an important part in the scientific life of his country and in the world of physics.
  
  Kramers won the Lorentz Medal in 1947 and Hughes Medal in 1951.
  
  Kramers received honorary degrees from the universities of Oslo, Lund, Stockholm, and the Sorbonne.

Works

More photos

• book

  • Collected Scientific Papers 1956

Views

During his years at Copenhagen, Kramers worked mainly on the further development of the quantum theory of the atom. In his doctoral thesis at Leiden in 1919 Kramers developed the mathematical formalism required to apply these ideas; he also carried out detailed calculations for the case of a hydrogen atom in an external electric field. This led to a satisfactory interpretation of the intensities of Stark components.

Other papers from this period deal with the relativistic theory of the Stark effect in hydrogen (1920), the continuous X-ray spectrum (1923), and the quantization of the rotation of molecules when there is a “built-in flywheel.” His paper on the helium atom (1923) was of special importance for the development of quantum theory. In this paper, Kramers showed that the application of the theory of quantization of classical orbits to the fundamental state of helium does not lead to a stable state and gives far too low a value for the binding energy. He pointed out that this revealed the fundamental inadequacy of the provisional quantum theory. From then on, the helium atom became a test case for a new theory. Eventually this challenge was successfully met by the new quantum mechanics, as was shown by W. Heisenberg and, with greater numerical precision, by Hylleraas.

Kramers was a coauthor of the famous paper by Bohr, Kramers, and J. C. Slater (1924) which suggested that conservation of energy might not hold in elementary processes. Although this idea was not substantiated by subsequent experimental and theoretical work, the paper had a profound influence. It emphasized the notion of virtual oscillators associated with quantum transitions. This concept formed the basis for Kramers’ theory of dispersion.

Kramers developed a special formalism for dealing with the theory of the multiplet structure of spectra (1930). It was based on Weyl’s treatment of the rotation group combined with notations current in the theory of invariants.

With G.P.Ittmann, Kramers studied the Schrodinger equation of the asymmetric top and made several additions to the theory of Lamé functions (1933,1938). In a very elegant paper (1935) he dealt with the solutions and eigenvalues of the Schrodinger equation for a particle in a one-dimensional periodic force field.

Kramers showed in a very general way that there exists an infinite number of zones of allowed energy values separated by forbidden regions. In many of these papers, Kramers is as much a mathematician as a physicist. Also his textbook on quantum mechanics (1933, 1938) contains a wealth of mathematical detail not found elsewhere. It is even more valuable, however, because it analyzes very carefully the basic principles and assumptions of quantum mechanics. A second group of papers dealt with paramagnetism, magneto-optical rotation, and ferromagnetism.

Two of Kramers’ papers (1934, 1936) dealt with ferromagnetism and the theory of spin waves; they formed the transition to a third group of papers - those dealing with statistical and kinetic theory. With Wannier, Kramers studied the two-dimensional Ising model.

Kramers and J. Kistemaker made an important contribution to the kinetic theory of gases (1943,1949). Maxwell had already shown that the aerodynamic boundary condition, according to which the velocity of a gas at the surface of a wall is equal to the velocity of the wall, is not strictly valid when there is a velocity gradient perpendicular to the wall or a temperature gradient along the wall; Maxwell had calculated in 1879 both this viscosity slip and the thermal slip. Kramers noticed that there should also be a diffusion slip which occurs when there is a concentration gradient along the wall. This would lead to a pressure gradient’s arising in a stationary state of diffusion through a capillary, and experiments confirmed this prediction.

Mention should also be made of an early contribution to the theory of strong electrolytes (1927), of a paper on the behavior of macromolecules in inhomogeneous flow (1946), and a very instructive paper on the use of Gibbs’s “grand ensemble” (1938).

Finally there were also a number of papers on relativistic formalisms in particle theory and on the theory of radiation. Kramers’ report to the 1948 Solvay Congress, entitled “Nonrelativistic Quantum Electrodynamics and Correspondence Principle” summarized ideas that had already been presented in his textbook on quantum mechanics (1933, 1938). His aim was to arrive at structure-independent results, and his method involved a separation between the proper field of the electron and the external field. To a certain extent these considerations have been superseded by later developments of quantum electrodynamics.

Membership

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.

Personality

Kramers greatly enjoyed music and could play the cello and the piano.

Interests

• cello, piano

Connections

On October 25, 1920, Kramers married Anna Petersen. They had three daughters and one son.

Father:

Hendrik Kramers

Mother:

Jeanne Susanne Breukelman

Spouse:

Anna Petersen

teacher:

Paul Ehrenfest

teacher:

Niels Bohr

colleague:

J. Kistemaker

colleague:

J. C. Slater

References

• Dictionary of Scientific Biography, Volume 7
  1973