Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid

Details Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid

2007-04-18

arxiv.org/abs/0704.2339v4

Physics

General Physics

11 pages; changed content

Scientific paper

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.

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