# ON KOOPMAN–VON NEUMANN WAVES II

@article{Mauro2001ONKN, title={ON KOOPMAN–VON NEUMANN WAVES II}, author={D. Mauro}, journal={International Journal of Modern Physics A}, year={2001}, volume={17}, pages={1475-1493} }

In this paper, we continue the study started in Ref. 1, of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the 1930s. In particular, we show that the introduction of the KvN Hilbert space of complex and square integrable "wave functions" requires an enlargement of the set of the observables of ordinary classical mechanics. The possible role and the meaning of these extra observables is briefly indicated in this work. We also analyze the similarities…

## 26 Citations

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This paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

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This paper extends the Madelung–Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform…

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