Koopman–von Neumann classical mechanics

The Koopman–von Neumann (KvN) theory is a description of classical mechanics as an operatorial theory similar to quantum mechanics, based on a Hilbert space of complex, square-integrable functions representing classical observables on phase spaces. As its name suggests, the KvN theory was developed by Bernard Koopman and John von Neumann.

The KvN theory is mathematically related to the conceptually distinct method of classical wavefunctions originally introduced by Mario Schönberg and others. These two methods will collectively be called Hilbert-space formulations of classical mechanics in what follows.