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Using quantum-classical analogies, we find that dynamical pictures of quantummechanics have precise counterparts in classical mechanics. In particular, theEulerian and Lagrangian descriptions of fluid dynamics in classical mechanicsare the analogs of the Schroedinger and Heisenberg pictures in quantummechanics, respectively. Similarities between classical and quantum dynamicalpictures are explored within the framework of the Koopman-von Neumannformalism. These allow for a natural definition of various dynamical picturesin classical mechanics as well as the application of classical concepts toquantum dynamics. As an illustration, we use the interaction picture to findthe classical evolution of an ensemble of particles of equal initial momentaand arbitrary configuration density under the action of a constant force in onedimension. As a second example, we discuss the extension of the ideas ofsensitivity to initial conditions and chaos in classical mechanics to quantummechanics.

Euler & Lagrange versus Heisenberg & Schroedinger: Dynamical Pictures in Classical and Quantum Mechanics

Euler & Lagrange versus Heisenberg & Schroedinger: Dynamical Pictures in Classical and Quantum Mechanics