What is the limit $\hbar \to 0$ of quantum theory ?

TL;DR

This paper examines the classical limit of quantum mechanics as Planck's constant approaches zero, revealing that Schrödinger's equation generally does not reduce to Newtonian mechanics, challenging assumptions about their direct connection.

Contribution

It demonstrates that the classical limit of quantum mechanics is not straightforward and that Schrödinger's equation does not universally lead to classical Newtonian mechanics as  approaches zero.

Findings

Schrödinger's equation does not generally yield Newton's laws in the  limit

Classical mechanics cannot be simply derived from quantum mechanics by taking 

The limit  is insufficient for classical emergence in quantum theory

Abstract

An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown that Schr\"odinger's equation for a single particle moving in an external potential $V$ does not, except in special cases, lead, in this limit, to Newton's equation of motion for the particle. This shows that classical mechanics cannot be regarded as emerging from quantum mechanics-at least in this sense-upon straightforward application of the limit $\hbar \to 0$.