Abstract
The theory of the semiclassical evolution of wave packets is developed as a version of WKB theory in phase space. Special attention is given to the transformation properties of wave packets, their Wigner functions, and their classical analogs under operations in phase space. A complete development of the Heisenberg and metaplectic operators is presented, including their interaction with the Wigner-Weyl formalism and the question of caustics. A metaplectically covariant wave packet propagator is presented and discussed. Finally, a group theoretical discussion of Gaussian wave packets is given.
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