Solitons and Quantum Behavior

Abstract

In applied physics and in engineering intuitive understanding is a boost for creativity and almost a necessity for efficient product improvement. The existence of soliton solutions to the quantum equations in the presence of self-interactions allows us to draw an intuitive picture of quantum mechanics. The purpose of this work is to compile a collection of models, some of which are simple, some are obvious, some have already appeared in papers and even in textbooks, and some are new. However this is the first time they are presented (to our knowledge) in a common place attempting to provide an intuitive physical description for one of the basic particles in nature: the electron. The soliton model applied to the electrons can be extended to the electromagnetic field providing an unambiguous description for the photon. In so doing a clear image of quantum mechanics emerges, including quantum optics, QED and field quantization. To our belief this description is of highly pedagogical value. We start with a traditional description of the old quantum mechanics, first quantization and second quantization. We describe an intuitive description of first and second quantization based on the concept of solitons, pioneered by the double solution of de Broglie in 1927. Many aspects of first and second quantization are clarified and visualized intuitively, including the so called vacuum fluctuations.