A duality in classical and quantum mechanics: General results

TL;DR

This paper uncovers a duality in classical and quantum mechanics, showing that dual systems within a family are interconnected through transforms, allowing solutions of one system to generate solutions for others.

Contribution

It introduces a general duality framework linking classical and quantum systems, enabling solution transfer within duality families.

Findings

Dual systems are related by duality transforms.

Solving one system in a duality family suffices to solve all others.

Duality unifies classical and quantum mechanics insights.

Abstract

We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other potentials are solved by the dual transform. That is, in a duality family, we only need to solve one system.