On the quantization of mechanical systems

TL;DR

This paper introduces a canonical method to quantize classical mechanical systems by assigning differential operators to classical magnitudes, establishing a rigorous correspondence principle and linking classical and quantum states.

Contribution

It provides a systematic approach to quantize classical systems and relates classical states to quantum wave equations, enhancing the theoretical foundation of quantum mechanics.

Findings

Established a canonical quantization procedure.

Linked classical states to quantum wave equations.

Demonstrated reciprocal conditioning between classical and quantum states.

Abstract

We present a canonical way of assigning to each magnitude of a classical mechanical system a differential operator in the configuration space, thus rigorously establishing the Correspondence Principle for such systems. Here we show how each classical state given in the whole system determine, for each classical magnitude, a wave equation, whose solutions are the possible quantum states for the given state and classical magnitude. Classical states and quantum states corresponding with the same system are reciprocally conditioned.