Elsevier, 1960. - 304 pp. In the present work, after a summary of the purely probabilistic interpretation, which is now "orthodox", and the objections to it put forward by a small but outstanding group of scientists, there will be found a general exposition of the present state of the theory of the Double Solution, the theory which is based on some early ideas of de Broglie and which was developed by him since 1951. According to this "causal interpretation", Wave Mechanics required a set of two coupled solutions of the wave equation: one, the Psi-wave, definite in phase, but, because of the continuous character of its amplitude, having only a statistical and subjective meaning; the other, the u-wave of the same phase as the Psi-wave but with an amplitude having very large values around a point in space and which, precisely on account of its spatial singularity (a singularity, moreover, which may not be one in the strict mathematical sense of the term) can be used to describe the particle objectively. So the theory gives a picture of the particle in which it appears as the center of an extended wave phenomenon involving the particle in an intimate way. It appears that the equation of the propagation of the u-wave is, basically, non-linear and, consequently, different from that admitted for the Psi-wave, even though the two equations may be considered identical almost everywhere.
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