Classical equations of motion and algebras of quantum observables

TL;DR

This paper introduces a straightforward quantization method for classical dynamical systems using differential equations, demonstrated through various examples, to bridge classical and quantum descriptions.

Contribution

It presents a novel, simple quantization approach based solely on differential equations describing system evolution.

Findings

Effective quantization procedure demonstrated on multiple examples

Bridges classical and quantum dynamics through differential equations

Provides a practical method for quantizing classical systems

Abstract

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.