Quantum Mechanics Without a Hamiltonian Operator

  • Adrian WüthrichEmail author
Part of the Archimedes book series (ARIM, volume 26)


In the early 1940s, when Feynman was a graduate student, one of the most pressing problems facing theoretical physicists of the time was the fact that infinite and, therefore, uninterpretable quantities arose from some of the principles of electrodynamics—in both classical electrodynamics as well as in the early attempts to establish a quantum theory.1 Roughly, the problem was as follows: an extended electron could not be stable because the charges distributed over its volume would repel each other. On the other hand, a point-like electron would imply that the energy contained in the electron’s electrostatic field would be infinite, since the field energy e/r diverges in the limit of vanishing radius r of the spatial distribution of the charge e.2


Wave Function Dirac Equation Classical Action Gordon Equation Classical Electrodynamic 
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  1. Helium. (Early 1950s). Series of selected folios from Box 11, Folder 6.Google Scholar
  2. Dirac, P. A. M. (1933). ‘The Lagrangian in Quantum Mechanics’. In: Physikalische Zeitschrift der Sowjetunion 3.1, pp. 64–72.Google Scholar
  3. Dirac, P. A. M. (1935). The Principles of Quantum Mechanics by P. A. M. Dirac. 2nd ed. Oxford: Clarendon Press.Google Scholar
  4. Dirac, P. A. M. (1938). ‘Classical Theory of Radiating Electrons’. In: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 167.929 (Aug. 1938), pp. 148–169.Google Scholar
  5. Fermi, E. (1932). ‘Quantum Theory of Radiation’. In: Reviews of Modern Physics 4.1 (Jan. 1932), pp. 87–132.CrossRefGoogle Scholar
  6. Feynman, R. P. (1949). ‘The Theory of Positrons’. In: Physical Review 76.6 (Sept. 1949), pp. 749–759.MathSciNetCrossRefGoogle Scholar
  7. Feynman, R. P. (2005). ‘The Principle of Least Action in Quantum Mechanics’. In: Feynman’s Thesis: A New Approach to Quantum Theory. Ed. by L. M. Brown. Singapore: World Scientific Publishing, pp. 1–69.Google Scholar
  8. Frenkel, J. (1925). ‘Zur Elektrodynamik punktförmiger Elektronen’. In: Zeitschrift für Physik A Hadrons and Nuclei 32.1 (Dec. 1925), pp. 518–534.ADSGoogle Scholar
  9. Frisch, M. (2005). Inconsistency, Asymmetry, and Non-Locality: A Philosophical Investigation of Classical Electrodynamics. Oxford: Oxford University Press.CrossRefGoogle Scholar
  10. Gleick, J. (1992). Genius: The Life and Science of Richard Feynman. Originally published: New York: Pantheon Books/Vintage Books.Google Scholar
  11. Pauli, W. (1933). ‘Die allgemeinen Prinzipien der Wellenmechanik’. In: Handbuch der Physik. Vol. 24: Quantentheorie. Ed. by H. Geiger and K. Scheel. Berlin: Springer, pp. 83–272.Google Scholar
  12. Schweber, S. S. (1994). QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga. Princeton: Princeton University Press.zbMATHGoogle Scholar
  13. Schwinger, J. (1948b). ‘Quantum Electrodynamics. I. A Covariant Formulation’. In: Physical Review 74.10 (Nov. 1948), pp. 1439–1461.MathSciNetCrossRefGoogle Scholar
  14. Shapere, D. (1984). ‘Notes Toward a Post-Positivistic Interpretation of Science, Part II’. In: Reason and the Search for Knowledge. Ed. by D. Shapere. Dordrecht: Reidel, pp. 352–382.Google Scholar
  15. Weiner, C. (1966b). ‘Interview with Dr. Richard Feynman, March 4 to June 28, 1966, Vol. 1’. Niels Bohr Library & Archives, American Institute of Physics, College Park, MD.Google Scholar
  16. Wheeler, J. A. and R. P. Feynman (1945). ‘Interaction with the Absorber as the Mechanism of Radiation’. In: Reviews of Modern Physics 17.2–3 (Apr. 1945), pp. 157–181.CrossRefGoogle Scholar
  17. ‘Minutes of the Cambridge, Massachusetts, Meeting, February 21 and 22, 1941’ (1941). In: Physical Review 59.8 (Apr. 1941), pp. 682–691.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.University of Bern, History and Philosophy of Science, Exact SciencesBernSwitzerland

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