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Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?

  • E. P. Wigner
Chapter
Part of the The Scientific Papers book series (WIGNER, volume A / 3)

Abstract

The commutator of the Hamiltonian with the operator corresponding to any physical quantity gives the operator which corresponds to the time derivative of that quantity. One can ask, hence, whether the postulate, that the quantum mechanical operators obey the classical equations of motion, uniquely determines the commutation relations. The answer is found to depend on the form of the Hamiltonian and is in the negative for a free particle and for the harmonic oscillator.

Reference

  1. E. Schrödinger, Abhandlungen zur Wellenmechanik (J. A. Barth, Leipzig, 1927 ).Google Scholar
  2. P. Ehrenfest, Zeits. f. Physik 4, 455 (1927).ADSCrossRefGoogle Scholar
  3. W. Heisenberg, Zeits. f.Physik 123, 93 (1944), p. 108 ff.Google Scholar
  4. W. Heisenberg see reference 3; A. Pais and S. Uhlenbeck (to be published).Google Scholar
  5. M. Born and P. Jordan, Zeits. f. Physik 34, 858 (1927).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • E. P. Wigner

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