On de Broglie's quantum particle as the soliton solution of linear Schrödinger equation

Details On de Broglie's quantum particle as the soliton solution of linear Schrödinger equation On de Broglie's quantum particle as the soliton solution of linear Schrödinger equation

2007-04-13

arxiv.org/abs/0704.1726v2

Physics

General Physics

14 pages, content changed

Scientific paper

We develop a class of soliton solution of {\it linear} Schr\"odinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by the velocity of the particle as firstly conjectured by de Broglie. Assuming resonance of the internal vibration will lead to quantization of particle's momentum in term of wave number of the envelope quantum probability density. We further show that the linearity of the Schr\"odinger equation allows us to have non-interacting many solitons solution through superposition, each describing a particle with equal mass.

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