On the fundamental structure of quantum mechanics

TL;DR

This paper argues that the core mathematical structures of quantum and classical mechanics are fundamentally similar, with differences arising mainly from their interpretations rather than their formal models.

Contribution

It demonstrates that quantum and classical models share the same mathematical framework for integrable systems, challenging the view of their fundamental disparity.

Findings

Quantum and classical models are mathematically equivalent for integrable systems.

Differences between quantum and classical mechanics stem from interpretative aspects.

The core mathematical structures of both theories are fundamentally similar.

Abstract

We show that there is no real difference between mathematical models of quantum mechanics and classical mechanics concerning integrable dynamical systems because the main difference between them results from their different interpretations.