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Abstract
Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics
have precise counterparts in classical mechanics. In particular, the Eulerian and
Lagrangian descriptions of fluid dynamics in classical mechanics are the analogs of
the Schroedinger and Heisenberg pictures in quantum mechanics, respectively. Similarities
between classical and quantum dynamical pictures are explored within the framework
of the Koopman-von Neumann formalism. These allow for a natural definition of various
dynamical pictures in classical mechanics as well as the application of classical
concepts to quantum dynamics. As an illustration, we use the interaction picture to
find the classical evolution of an ensemble of particles of equal initial momenta
and arbitrary configuration density under the action of a constant force in one dimension.
As a second example, we discuss the extension of the ideas of sensitivity to initial
conditions and chaos in classical mechanics to quantum mechanics.