Time-dependent Schr\"odinger equation from the Hamilton-Jacobi equation

TL;DR

This paper explores the derivation of the time-dependent Schrödinger equation starting from the Hamilton-Jacobi equation, aiming to connect classical and quantum mechanics through mathematical reformulation.

Contribution

It introduces a novel approach to derive the Schrödinger equation from classical Hamilton-Jacobi formalism, bridging classical and quantum descriptions.

Findings

Established a formal link between Hamilton-Jacobi and Schrödinger equations

Provided a new perspective on quantum dynamics derivation

Potential implications for quantum-classical correspondence

Abstract

This paper and abstract have been withdrawn.