Rauh, Alexander (2018) Quantum mechanics of rectilinear orbits of the Coulomb-Kepler problem (II.). Advanced studies in theoretical physics, 12 (3). pp. 129-150. ISSN 1313-1311

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Official URL: http://dx.doi.org/10.12988/astp.2018.838

Abstract

As compared to the wave function adopted previously (Adv. Stud. in Theor. Phys. Vol.11, 2017, p.365), the new ansatz for fulills now energy conservation rigorously with respect to a curve parameter w greater/equal 0. The symmetry of implies that the mean position and mean velocity are parallel or anti-parallel, always. The model describes the scattering of a wave packet by the Coulomb potential over a finite time range, where in the mean only forward and back scattering is possible. The decisive point is to elaborate the definition interval of w as a time equivalent curve parameter. The mean initial position and velocity are built into and form a two-dimensional parameter space P. As it turns out, within a subspace A _ P, curve parameter w and time t are in 1-1 correspondence for all t greater/equal 0; moreover, one observes mean forward scattering when the mean initial velocity is directed towards the force center: the mean trajectory "tunnels" through the Coulomb singularity. On the other hand, in the parameter space complementary to A, the definition domain of the curve parameter is limited and ends before the singularity is reached, which means that forward or backscattering cannot be predicted by the given model where the time dependent Schrödinger equation is not generally solved.

Item Type: Article
Additional Information: Publiziert mit Hilfe des DFG-geförderten Open Access-Publikationsfonds der Carl von Ossietzky Universität Oldenburg.
Subjects: Science and mathematics > Physics
Divisions: Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited: 11 Sep 2019 10:20
Last Modified: 25 Sep 2019 11:11
URI: https://oops.uni-oldenburg.de/id/eprint/4141
URN: urn:nbn:de:gbv:715-oops-42226
DOI: doi:10.12988/astp.2018.838
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