We consider the dynamics of a quantum joint phase-space probability density in an exactly solvable model. The density is defined to be a true (i.e., positive) probability distribution for approximate (and thus simultaneously measurable) position and momentum variables. The dynamics of the quantum density is governed by a second-order partial-differential equation with non-positive-definite second-order coefficients. The quantum dynamics is contrasted with the dynamics of a similar joint density in a classical description. The non-positive-definite second-order terms in the quantum evolution equation, not present in the classical case, are responsible for quantum recurrences and prevent the appearance of fine-scale-structure ‘‘whorls’’ predicted in a classical description. The generation of ‘‘squeezing’’ in the model is also discussed.

• Received 29 April 1985

DOI:https://doi.org/10.1103/PhysRevA.33.674