On Koopman-von Neumann Waves

Abstract

In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently than what happens in quantum mechanics. The role of the phases associated to these classical "wave functions" is analyzed in details. In this framework we also perform the analog of the two-slit experiment and compare it with the quantum case.Comment: 27+1 pages, 2 figure