2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36303The 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.6 pages, no figures; Minor changes which do not affect the general results and conclusions. To appear in ApeironGeneral Relativity and Quantum Cosmologytext