Generalized guidance equation for peaked quantum solitons: the single particle case
Abstract
We study certain non-linear generalisations of the Schr{\"o}dinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schr{\"o}dinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schr{\"o}dinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.
Keywords
Cite
@article{arxiv.1602.03133,
title = {Generalized guidance equation for peaked quantum solitons: the single particle case},
author = {Thomas Durt},
journal= {arXiv preprint arXiv:1602.03133},
year = {2016}
}
Comments
The second version of this paper will be published in 2017 in a special issue devoted to the Double Solution Program of Louis de Broglie under the title: "de Broglie's double solution and self-gravitation"