Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid
General Physics
2009-08-19 v4
Abstract
We show in spatially one dimensional Madelung fluid that a simple requirement on local stability of the maximum of quantum probability density will, if combined with the global scale invariance of quantum potential, lead to a class of quantum probability densities globally being self-trapped by their own self-generated quantum potentials, possessing only a finite-size spatial support. It turns out to belong to a class of the most probable wave function given its energy through the maximum entropy principle. We proceed to show that there is a limiting case in which the quantum probability density becomes the stationary-moving soliton-like solution of the Schr\"odinger equation.
Cite
@article{arxiv.0704.2339,
title = {Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid},
author = {Agung Budiyono},
journal= {arXiv preprint arXiv:0704.2339},
year = {2009}
}