Introduction to Koopman-von Neumann Mechanics

TL;DR

This paper provides a clear overview of Koopman-von Neumann Mechanics, a classical mechanics framework expressed in quantum language, highlighting its mathematical structure, applications, and role in understanding quantum-classical relationships.

Contribution

It consolidates and simplifies existing literature on KvN Mechanics, making it accessible and emphasizing its significance in statistical physics and quantum-classical studies.

Findings

KvN Mechanics uses Hilbert phase space and operators.

It is a valuable tool in statistical physics.

Numerous applications of KvN have been developed recently.

Abstract

This work is to consolidate current literature on Koopman-von Neumann (KvN) Mechanics into a simple and easy to understand text. KvN Mechanics is a branch of Classical Mechanics that has been recast into the mathematical language of Quantum Mechanics. KvN Mechanics utilizes a Hilbert phase space with operators to calculate the expectation values of observables of interest (expectation values such as position, momentum, etc.) It is an important tool in statistical physics and guide to illuminate the mysterious relationship between Quantum and Classical Physics. A lot of important applications of KvN Mechanics have been developed in the last decade.