Factorizations of one dimensional classical systems

TL;DR

This paper characterizes a class of one-dimensional classical systems through algebraic factorization, revealing their integrals of motion and phase dynamics, analogous to quantum factorizable systems.

Contribution

It introduces an algebraic framework for classical systems using Hamiltonian factorization and Poisson algebra closure, bridging classical and quantum factorizable systems.

Findings

Hamiltonians are factorized into two functions

Two time-dependent integrals of motion are derived

Classical systems are analogous to quantum factorizable systems

Abstract

A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra. These two functions lead directly to two time-dependent integrals of motion from which the phase motions are derived algebraically. The systems so obtained constitute the classical analogues of the well known factorizable one dimensional quantum mechanical systems.