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
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.
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