  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.
