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The formulation of quantum mechanics in terms of phase space functions-the third equation

1991; Institute of Physics; Volume: 24; Issue: 16 Linguagem: Inglês

10.1088/0305-4470/24/16/018

1361-6447

D. B. Fairlie, Corinne A. Manogue,

Algebraic structures and combinatorial models

The formalism of the Wigner distribution function is reviewed. In addition to the Liouville equation, which expresses the time rate of change of this function in terms of its Moyal bracket with the Hamiltonian, and its expression as a projection operator, a third equation is proposed with the aid of an auxiliary variable s, to which a formal solution is constructed in terms of known quantum-mechanical eigenfunctions and eigenvalues. In addition, an ab initio solution to the three equations in terms of an error function is found for the free particle in one dimension. Two views are advanced: the orthodox, that this new equation is merely a consistency requirement, and the speculative, that the measurement process has something to do with the choice of s.