A set of quasi-proba.bility distribution functions which give the correct quantum mecha.nical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state fUDction. The Wigner distribution is a special case. A general relationship between the pbase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will, of which the ones presently known are particular cases. The dynamics and other properties of the generalized pbase-space distribution are considered.
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