Kramers’s Contributions to Statistical Mechanics
DOI: 10.1063/1.881132
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.
References
1. M. Dresden, H. A. Kramers: Between Tradition and Revolution, Springer‐Verlag, New York (1987).
2. J. C. Maxwell, Scientific papers, vol. 2, W. D. Niven, ed., Cambridge U.P., Cambridge (1890), p. 401.
3. M. J. Klein, Physica A 106, 3 (1981).https://doi.org/PHYADX
4. H. A. Kramers, Collected Works, North Holland, Amsterdam (1956), p. 887.
5. D. ter Haar, Elements of Statistical Mechanics, Rinehart, New York (1954).
6. J. Vlieger, interview with M. Dresden.
7. G. Heller, Proc. Acad. Amsterdam 37, 378 (1934).
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/PHRVAO9. H. A. Kramers, Commun. Kamerlingh Onnes Lab. 22, suppl. 83, 1 (1936).
10. H. A. Kramers, J. Kistemaker, Physica 10, 699 (1943).https://doi.org/PHYSAG
11. H. A. Kramers, Physica 7, 284 (1940).https://doi.org/PHYSAG
12. D. Wyckoff, N. Balasz, Physica A 146, 175 (1987).https://doi.org/PHYADX
13. R. Landauer, Helv. Phys. Acta 56, 847 (1983).https://doi.org/HPACAK
14. M. Buttiker, E. P. Harris, R. Landauer, Phys. Rev. B 28, 1268 (1983).https://doi.org/PRBMDO
15. H. C. Brinkman, Physica 22, 149 (1956).https://doi.org/PHYSAG
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.
