Abstract
By means of the Weyl transform we propose to associate phase-spaceoperators, and not functions with the dynamical operators of quantum-mechanics. This way one achieves a consistent and one-to-one mapping of the quantum-mechanical operator calculus unto a phase-space operator calculus in which only variables associated with the canonical variables of position and momenta appear. Contrary to the usual Weyl transform technique, here no composition law is needed for the Weyl transforms. As a consequence the calculus involving Weyl transforms is greatly simplified, which we demonstrate at two examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Weyl, H.: Z. Physik46, 1 (1927)
Wigner, E.: Phys. Rev.40, 749 (1932)
Moyal, J.E.: Proc. Camb. Phil. Soc.45, 99 (1949)
Balazs, N.L., Pauli, H.C.: Z. Physik A277, 265 (1976)
deGroot, S.: La transformation de Weyl et la fonction de Wigner, Les Presses de l'Université de Montreal 1974
Irving, J.H., Zwanzig, R.W.: J. Chem. Phys.19, 1173 (1951)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Balazs, N.L., Pauli, H.C. Quantum-mechanical operators and phase-space operators. Z Physik A 282, 221–225 (1977). https://doi.org/10.1007/BF01408166
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01408166