Abstract
The exact agreement between the Sommerfeld and Dirac results for the energy levels of the relativistic hydrogen atom (the “Sommerfeld Puzzle”) is analyzed and explained.
Similar content being viewed by others
References
A. J. W. Sommerfeld,Ann. d. Physik 50, 1 (1916).
C. G. Darwin,Proc. Roy. Soc. 118, 654 (1928); W. Gordon,Z. f. Physik 48, 11 (1928).
W. Yourgrau and S. Mandelstam,Variational Principles in Dynamics and Quantum Theory (W. B. Saunders Co., Philadelphia, 1968), 3rd ed.
Letter to Yourgrau-Mandelstam, dated 29/II/56 and quoted, loc. cit. ref. (3), p. 113 ff. The italics are in the original.
Loc. cit. (Ref. 3 ), p. 115.
Oxford English Dictionary (Oxford Univ. Press, 1971).
Loc. cit. p. 14.
A. Sommerfeld,Sitzungsberichte der Münchener Akademie, Dec. 1915; Jan. 1916.
W. Wilson,Phil. Mag. 31, 161 (1916).
A. Sommerfeld,Atombau und Spektrallinien (Vieweg, Braunschweig, 1929), 5th ed. Only the third edition of this work (translated by H. L. Brose),Atomic Structure and Spectral Lines (Methuen, London, 1923) contains the geometric approach. See pp. 467–475.
L. C. Biedenharn and P. J. Brussaard,Coulomb Excitation (Clarendon Press, Oxford, 1965).
A. O. Barut,Dynamical Groups and Generalized Symmetries in Quantum Theory, Univ. of Canterbury (Christchurch, NZ, 1971).
E. P. Wigner,Group Theory and the Special Functions of Mathematical Physics, Lecture Notes, Princeton, 1955 (unpublished).
H. Bacry and J. L. Richard,J. Math. Phys. 8, 2230 (1967).
P. A. M. Dirac,Principles of Quantum Mechanics (Clarendon Press, Oxford, 1947).
L. C. Biedenharn,Phys. Rev. 126, 845 (1961).
G. Temple,The General Principles of Quantum Mechanics (Methuen and Co., New York, 1948). See also remarks added in proof, Ref. 20.
M. H. Johnson and B. A. Lippmann,Phys. Rev. 78, 329 (1950).
E. P. Wigner,Rev. Mod. Phys. 29, 255 (1957).
L. C. Biedenharn and N. V. V. J. Swamy,Phys. Rev. 133, B1353 (1964).
I. A. Malkin and V. I. Manko,Zh. Ekps. Teor. Fiz. 55, 287 (1968).
L. C. Biedenharn, M. Y. Han, and H. van Dam,Phys. Rev. D6, 500 (1972).
Author information
Authors and Affiliations
Additional information
Research supported in part by the National Science Foundation.
Rights and permissions
About this article
Cite this article
Biedenharn, L.C. The “Sommerfeld Puzzle” revisited and resolved. Found Phys 13, 13–34 (1983). https://doi.org/10.1007/BF01889408
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889408