The de Broglie Waves of Matter and Properties of the Quantum Ensembles

The de Broglie waves of matter are applied in examination of the quantum ensembles. In the first step it is pointed out that the formula for the density of photons in a cavity is much similar to that for the density of electrons in the free-electron gas. If a minimal oscillation time period deduced from the uncertainty principle for energy and time is applied to photons, the maximal momentum of the photon ensemble approaches the expression for a maximal electron momentum deduced from the special theory of relativity. The de Broglie waves were applied also to examine the plasmons exhibited by the many-electron ensembles. A density limit of the electron gas is obtained below of which the presence of plasmons can be admitted. The ratio of this density limit to the limit calculated on the basis of the energy-time principle of uncertainty attains one-third of the reciprocal value of the atomic constant.