Spreading of wave packets, Uncertainty Relations and the de Broglie Frequency

TL;DR

This paper investigates the spreading of quantum wave packets in free and harmonic oscillator scenarios, revealing a connection between zero-point energy and the de Broglie frequency through uncertainty relations.

Contribution

It introduces a novel analysis linking wave packet spreading, uncertainty principles, and de Broglie frequency in quantum mechanics.

Findings

Wave packet width increases over time for free particles.

Zero-point energy corresponds to the de Broglie frequency.

Conservation of packet width leads to new insights on quantum energy levels.

Abstract

The spreading of quantum mechanical wave packets is studied in two cases. Firstly we look at the time behavior of the packet width of a free particle confined in the observable Universe. Secondly, by imposing the conservation of the time average of the packet width of a particle driven by a harmonic oscillator potential, we find a zero-point energy which frequency is the de Broglie frequency.