Discover
/
Article

Kramers’s Contributions to Statistical Mechanics

SEP 01, 1988
Remarks and comments scattered in papers by Hendrik A. Kramers laid the conceptual foundations for the theory of phase transitions and led to the solution of the two‐dimensional Ising model.
Max Dresden

Hendrik A. Kramers was a major figure in the long and painful struggle that propelled quantum physics from the inspired but artful guessing game of the Bohr rules to a well‐defined, coherent and systematic quantum mechanics. Kramers’s basic and deep contributions in this struggle are barely known nowadays, and he actually suffers in comparison with Niels Bohr and Louis de Broglie, let alone Paul Dirac, Werner Heisenberg and Wolfgang Pauli. Kramers is still known for a number of isolated and disconnected results, such as the WKB method, the Kramers degeneracy in magnetism and the Kramers‐Kronig relations. Although these are unquestionably significant and first‐rate contributions, they do not demonstrate Kramers’s deep physical insight and his profound concern for fundamental questions. They show Kramers as an extraordinarily skillful craftsman rather than as a scientific innovator. This may be an important reason why Kramers’s reputation has faded so markedly in comparison with those of, say, Heisenberg or Pauli, whose contemporary he was and who, as his fellow architects of quantum mechanics, recognized him as a talented physicist and deep thinker. For example, when Bartel L. van der Waerden started to collect what he believed were the seminal papers in quantum mechanics, Pauli, hardly a person known for his generosity in giving undeserved credit, alerted him to the importance of Kramers’s investigations.

This article is only available in PDF format

References

  1. 1. M. Dresden, H. A. Kramers: Between Tradition and Revolution, Springer‐Verlag, New York (1987).

  2. 2. J. C. Maxwell, Scientific papers, vol. 2, W. D. Niven, ed., Cambridge U.P., Cambridge (1890), p. 401.

  3. 3. M. J. Klein, Physica A 106, 3 (1981).https://doi.org/PHYADX

  4. 4. H. A. Kramers, Collected Works, North Holland, Amsterdam (1956), p. 887.

  5. 5. D. ter Haar, Elements of Statistical Mechanics, Rinehart, New York (1954).

  6. 6. J. Vlieger, interview with M. Dresden.

  7. 7. G. Heller, Proc. Acad. Amsterdam 37, 378 (1934).

  8. 8. H. A. Kramers, G. Wannier, Phys. Rev. 60, 252 (1941). https://doi.org/PHRVAO
    H. A. Kramers, G. Wannier, Phys. Rev. 60, 263 (1941).https://doi.org/PHRVAO

  9. 9. H. A. Kramers, Commun. Kamerlingh Onnes Lab. 22, suppl. 83, 1 (1936).

  10. 10. H. A. Kramers, J. Kistemaker, Physica 10, 699 (1943).https://doi.org/PHYSAG

  11. 11. H. A. Kramers, Physica 7, 284 (1940).https://doi.org/PHYSAG

  12. 12. D. Wyckoff, N. Balasz, Physica A 146, 175 (1987).https://doi.org/PHYADX

  13. 13. R. Landauer, Helv. Phys. Acta 56, 847 (1983).https://doi.org/HPACAK

  14. 14. M. Buttiker, E. P. Harris, R. Landauer, Phys. Rev. B 28, 1268 (1983).https://doi.org/PRBMDO

  15. 15. H. C. Brinkman, Physica 22, 149 (1956).https://doi.org/PHYSAG

  16. 16. H. Friedman, M. D. Newton, J. Chem. Phys. 88, 7 (1988).

More about the Authors

Max Dresden. Institute for Theoretical Physics, State University of New York, Stony Brook.

Related content
/
Article
Figuring out how to communicate with the public can be overwhelming. Here’s some advice for getting started.
/
Article
Amid growing investment in planetary-scale climate intervention strategies that alter sunlight reflection, global communities deserve inclusive and accountable oversight of research.
/
Article
Although motivated by the fundamental exploration of the weirdness of the quantum world, the prizewinning experiments have led to a promising branch of quantum computing technology.
/
Article
As conventional lithium-ion battery technology approaches its theoretical limits, researchers are studying alternative architectures with solid electrolytes.
This Content Appeared In
pt-cover_1988_09.jpeg

Volume 41, Number 9

Get PT in your inbox

pt_newsletter_card_blue.png
PT The Week in Physics

A collection of PT's content from the previous week delivered every Monday.

pt_newsletter_card_darkblue.png
PT New Issue Alert

Be notified about the new issue with links to highlights and the full TOC.

pt_newsletter_card_pink.png
PT Webinars & White Papers

The latest webinars, white papers and other informational resources.

By signing up you agree to allow AIP to send you email newsletters. You further agree to our privacy policy and terms of service.