Foundations of Quantum Mechanics

Abstract

The physical significance of the waves which, according to de Broglie’s concept, are related to the motion of particles was not discovered immediately. Attempts were made at first to regard the particles themselves as consisting of waves and distributed in some region of space. The intensity of the de Broglie wave was regarded, on this view, as a quantity representing the density of the medium of which the particle was formed. This conception of de Broglie waves was an entirely classical one. It was based on the fact that in some very special cases it is theoretically possible to construct from waves structures whose motion coincides with that of a particle moving in accordance with the laws of classical mechanics. An example is the wave packet discussed above. As shown in Section 7, the centroid of a wave packet moves as a particle. However, the motion of such a wave packet does not entirely agree with that of a particle. The reason is that the shape of the wave packet changes in the course of time. As will be shown in Section 34, the size of the wave packet increases, and it is broadened out. The necessity of this is easily understood from the existence of dispersion of de Broglie waves in vacuo. The individual waves of which the wave packet is composed are propagated at different velocities, and in consequence the wave packet spreads out.