How to prepare quantum states that follow classical paths

TL;DR

This paper introduces an alternative quantization method for 1D quantum mechanics that produces non-dispersive wave packets closely following classical paths, maintaining minimum uncertainty for free particles.

Contribution

It proposes a new quantization approach that ensures wave packets align with classical trajectories and do not disperse, enhancing the classical-quantum correspondence.

Findings

Wave packets do not disperse and follow classical paths

Complete classical-quantum correspondence achieved for free particle and particle in a box

Wave packets satisfy minimum uncertainty relation for free particles

Abstract

We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be obtained using this formulation. The resulting wave packets do not disperse and strongly peak on the classical paths. Moreover, for the case of the free particle, they satisfy minimum uncertainty relation.