Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid
arXiv:0704.2339
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 Schrödinger equation.
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