Hamilton's Equations of Motion from Schr\"odinger's Equation

TL;DR

This paper demonstrates how classical Hamilton's equations of motion can be derived from Schrödinger's quantum equation through the process of wave function collapse in an environmentally entangled open quantum system.

Contribution

It introduces a novel derivation of classical dynamics directly from quantum mechanics using decoherence and wave function collapse mechanisms.

Findings

Hamilton's equations emerge from quantum wave function collapse.

Decoherence in open quantum systems leads to classical behavior.

Provides a bridge between quantum and classical descriptions.

Abstract

Starting from Schr\"odinger's equation, Hamilton's classical equations of motion emerge from the collapse of the unsymmetrized wave function in a decoherent open quantum system entangled with its environment.