Soliton-like solutions to the ordinary Schroedinger equation

Details Soliton-like solutions to the ordinary Schroedinger equation Soliton-like solutions to the ordinary Schroedinger equation

2010-08-17

arxiv.org/abs/1008.3087v2

Physics

Quantum Physics

31 pages, including 9 Figures; with a LaTeX source-file. Replaced by adding (in sect.4.1) several plots, which show new partic

Scientific paper

In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G and Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation, within standard Quantum Mechanics; and we obtain both approximate and exact solutions, setting forth particular examples for them. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we also demonstrate, therefore, how to obtain finite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. Some physical comments are added.

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