Quantum particles that behave as free classical particles

TL;DR

This paper demonstrates that certain quantum solutions, characterized by specific phases and probability densities, can behave as free classical particles despite quantum interactions, bridging quantum and classical dynamics.

Contribution

It introduces a method to construct quantum states that mimic free classical particles using solutions of the Schrödinger equation with non-vanishing Bohm potentials.

Findings

Quantum solutions propagate as free classical particles

Bohm potentials enable classical-like behavior in quantum states

Constructed solutions follow classical Hamilton-Jacobi dynamics

Abstract

The existence of non-vanishing Bohm potentials, in the Madelung-Bohm version of the Schr\"odinger equation, allows for the construction of particular solutions for states of quantum particles interacting with non-trivial external potentials that propagate as free classical particles. Such solutions are constructed with phases which satisfy the classical Hamilton-Jacobi for free particles and whose probability densities propagate with constant velocity, as free classical particles do.