Sommerfeld’s Contributions to Quantum Theory

  • Wolfgang Pauli


The early work of A. Sommerfeld had been concerned partly with applications of the mathematics of wave theory, such as the integration of Maxwell’s equations in problems of diffraction and wireless telegraphy, and partly with problems of classical electron theory. The X-rays emitted when electrons are decelerated had already brought him up against quantum theory; 1 and Voigt’s formal theory of the anomalous Zeeman effect of doublet spectra, which he was able to simplify substantially by considering emission instead of absorption, 2 had brought him into contact with the great complex of problems connected with the explanation of spectra. Shortly afterwards, through Bohr’s fundamental work (from 1913 onwards) Rutherford’s nuclear model of the atom was linked up with Planck’s quantum theory of thermal radiation, and Rydberg’s constant of spectra was reduced to the quantum of action and the charge and mass of the electron (with a supplementary correction for the motion of the nucleus). It was at the end of 1915 that Sommerfeld, greatly impressed by this new development, turned his attention to the theoretical interpretation of spectra and the associated problems of atomic structure. It can be said that this period marked the beginning of a new chapter in Sommerfeld’s scientific activity, which entailed not only a change in the object of study, but also a fundamental change in the methods employed in his work.


Quantum Number Quantum Theory Correspondence Principle Phase Integral Secular Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Sommerfeld, Report to the Solvay Congress, Brussels, 1911.Google Scholar
  2. 2.
    A. Sommerfeld, Göttinger Nachrichten, math.-phys. Klasse (1914).Google Scholar
  3. 3.
    A. Sommerfeld, Sitzungsberichte der Münchener Akademie der Wissenschaften, pp. 425, 459 (1915); p. 131 (1916). Annalen der Physik 51, 1, 125 (1916) (Quantum theory of spectral lines).Google Scholar
  4. 4.
    P. S. Epstein, Physikalische Zeitschrift 17, 148 (1916); Annalen der Physik 50, 489; 51, 168 (1916).Google Scholar
  5. 5.
    K. Schwarzschild, Sitzungsberichte der Berliner Akademie der Wissenschaften, phys. math. Klasse, p. 548 (1916); cf. also J. M. Burger’s Dissertation, Haarlem (1918).Google Scholar
  6. 6.
    M. Planck, Verhandlungen der Deutschen Physikalischen Gesellschaft 17, 407, 438 (1915); Annalen der Physik 50, 385 (1916).Google Scholar
  7. 7.
    N. Bohr, Kongelige Danske Videnskababernes Selskab Skrifter, naturvidensk og mat. Afd. 8 Raekke IV, 1, Parts I and II (1918); German translation by P. Hertz under the title Über die Quantentheorie der Linienspektren (Braunschweig 1923).Google Scholar
  8. 8.
    A. Sommerfeld, Physikalische Zeitschrift 17, 491 (1916) (Theory of the Zeeman effect of the hvdrogen lines. with an appendix on the Stark effect).Google Scholar
  9. 9.
    P. Debye, Physikalische Zeitschrift 17, 507 (1916).Google Scholar
  10. 10.
    A. Sommerfeld, Atombau und Spektrallinien. Vieweg, Braunschweig: 1 st ed. (1919); 2nd ed. (1920); 3rd ed. (1922); 4th ed. (1924); Wellenmechanischer Ergänzungsband (1929); 5th ed. Vol. I (1931), Vol. II (1939).* English translation by Henry L. Brose in A. Sommerfeld: Atomic Structure and Spectral Lines, London and New York, Dutton 1923.Google Scholar
  11. 11.
    A. Sommerfeld and W. Kossel, Verhandlungen der Deutschen Physikalischen Gesellschaft 21, 240 (1919) (Selection principle and displacement law in series spectra).Google Scholar
  12. 12.
    A. Sommerfeld, Die Naturwissenschaften 8, 61 (1920) (A numerical puzzle in the theory of the Zeeman effect).CrossRefADSGoogle Scholar
  13. 13.
    A. Sommerfeld, Annalen der Physik 63, 221 (1920) (General spectroscopic regularities, especially a magneto-optic decomposition rule).CrossRefADSGoogle Scholar
  14. 14.
    A. Sommerfeld, Zeitschriftfür Physik 8, 257 (1922) (Reinterpretation in terms of quantum theory of Voigt’s theory of the anomalous Zeeman effect in lines of the D type).CrossRefADSGoogle Scholar
  15. 15.
    A. Sommerfeld, Physikalische Zeitschrift 24, 360 (1923) (Spectroscopic magneton numbers); Zeitschrift für Physik 19, 221 (1923) (Theory of the magneton).Google Scholar
  16. 16.
    A. Sommerfeld, Annalen der Physik 70, 32 (1923) (Interpretation of complex spectra such as Mn, Cr etc. by the method of inner quantum numbers); Annalen der Physik 73, 209 (1924) (Theory of multiplets and their Zeeman effect).CrossRefADSGoogle Scholar
  17. 17.
    H. Hönl, Zeitschrift für Physik 31, 340 (1925).MATHCrossRefADSGoogle Scholar
  18. 18.
    S. Goudsmit and R. Kronig, Die Naturwissenschaften 13, 90 (1925).CrossRefADSGoogle Scholar
  19. 19.
    A. Sommerfeld and W. Heisenberg, Zeitschrift für Physik 11, 131 (1922) (Intensity of multiplet lines and their Zeeman components).CrossRefADSGoogle Scholar
  20. 20.
    A. Sommerfeld and H. Hönl, Sitzungsberichte der Berliner Akademie der Wissenschaften, phys.-math. Klasse, p. 141 (1925) (Intensity ofmultiplet lines); H. W. Russell, Nature 115, 835 (1925); Proceedings of the American Academy of Arts and Sciences 11, 314, 322 (1925); R. Kronig, Zeitschrift für Physik 31, 885 (1925).Google Scholar
  21. 21.
    A. Sommerfeld, Die Naturwissenschaften 15, 825 (1927); Zeitschrift für Physik 47, 1 (1928) (Electron theory of metals).MATHCrossRefADSGoogle Scholar
  22. 22.
    A. Sommerfeld and H. Bethe, Handbuch der Physik (Springer, Berlin) volume XXIV/2, 2nd ed., pp. 333–620 (1933) (Electron theory of metals). The first chapter of this report is by Sommerfeld himself.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Wolfgang Pauli

There are no affiliations available

Personalised recommendations