Formulation of Quantum Mechanics Based on the Quasi-Probability Distribution Induced on Phase Space

George A. Baker, Jr.
Phys. Rev. 109, 2198 – Published 15 March 1958
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Abstract

We postulate a formulation of quantum mechanics which is based solely on a quasi-probability function on the classical phase space. We then show that this formulation is equivalent to the standard formulation, and that the quasi-probability function is exactly analogous to the density matrix of Dirac and von Neumann. We investigate the theory of measurement in this formulation and derive the following remarkable results. As is well known, the correspondence between classical functions of both the position and conjugate momentum and quantum mechanical operators is ambiguous because of noncommutativity. We show that the solution of this correspondence problem is completely equivalent to the solution of the eigenvalue problem. This result enables us to give a constructive method to compute eigenvalues and eigenfunctions.

  • Received 25 March 1957

DOI:https://doi.org/10.1103/PhysRev.109.2198

©1958 American Physical Society

Authors & Affiliations

George A. Baker, Jr.*

  • University of California, Berkeley, California

  • *Now at Los Alamos Scientific Laboratory, Los Alamos, New Mexico.

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Issue

Vol. 109, Iss. 6 — March 1958

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