Theoretica chimica acta

, Volume 74, Issue 4, pp 323–330 | Cite as

The complete symmetrization of quantum operators: new thoughts on an old problem

  • André Julg


The complete symmetrization with respect to x, px,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A2)=(op A)2. For example, angular momentum operators M z 2 and M2 are modified by the additive constants ħ2/2 and 3ħ2/2 respectively (M2≠0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.

Key words

Interpretation of quantum mechanics Quantum operators 


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • André Julg
    • 1
  1. 1.Laboratoire de Chimie ThéoriqueUniversité de ProvenceMarseille-Cedex 3France

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