Imprints of the Quantum World in Classical Mechanics

TL;DR

This paper demonstrates that the Schrödinger equation for nonrelativistic spinless particles can be viewed as a classical Hamiltonian system, revealing deeper connections between quantum and classical mechanics without additional physical assumptions.

Contribution

It shows that the Schrödinger equation is equivalent to classical Hamilton's equations, highlighting the quantum imprints in classical mechanics without relying on physical hypotheses.

Findings

Schrödinger equation is equivalent to Hamilton's equations for certain systems

Quantum imprints are more extensive in classical mechanics than previously thought

No additional physical hypotheses are needed to establish this equivalence

Abstract

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.