Crtierion of effective centre-of-mass method in Quantum Mechanics

TL;DR

This paper discusses criteria for choosing between quantum and classical mechanics for atomic and cluster motion, emphasizing the effective centre-of-mass method and proposing an experiment to test the criteria.

Contribution

It clarifies the conditions under which the effective centre-of-mass method should be applied in quantum mechanics for atomic and cluster motion.

Findings

Quantum mechanics is appropriate when the de Broglie wavelength exceeds particle size.

The effective centre-of-mass method is valid under specific quantum conditions.

An experimental test is proposed to verify the criteria.

Abstract

In describing the motion of atoms and clusters, we face with choosing quantum mechanics or classical mechanics under different conditions. In principle, there exist two criteria for this choice, but they do contradict in some cases though they are in agreement for other cases. Actually, this problem is closely related with the effective centre-of-mass method, the underlying application of quantum mechanics. It is shown that quantum mechanics must be selected for particle's motion when the de Broglie wave length of the mass centre is larger than the particle size, and in such case the effective centre-of-mass can be used in Quantum Mechanics. In order to test this conclusion, an easy-manufactured experiment is suggested.