ON KOOPMAN–VON NEUMANN WAVES

2002/04/10 by D. MAURO, D. Mauro · 4 citations
Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Fluid Dynamics and Turbulent Flows #Mechanical and Optical Resonators

paper · doi:10.1142/s0217751x02009680

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 from what happens in quantum mechanics. The role of the phases associated to these classical "wave functions" is analyzed in detail. In this framework we also perform the analog of the two-slit interference experiment and compare it with the quantum case.

Cited by

• Solutions of Koopman-von Neumann equations, their superpositions, orthogonality and uncertainties
• The Particle in a Box in Koopman--von Neumann Mechanics: A Hilbert Space representation of Classical Mechanics
• Quantum field theory for classical fields
• ON KOOPMAN–VON NEUMANN WAVES II

Related

• ON KOOPMAN–VON NEUMANN WAVES II
• The history of Hilbert-space formulations of classical physics
• Topics in Koopman-von Neumann Theory
• Classical and mixed classical-quantum systems from van Hove's unitary representation of contact transformations
• On the Operator Origins of Classical and Quantum Wave Functions