Spreading of wave packets, Uncertainty Relations and the de Broglie   Frequency
  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. 
H.C.G. Caldas (FUNREI, Brasil), P.R. Silva (UFMG, Brasil)