51 research outputs found
Periodic systems in time: double-well potential
Time analysis of oscillations of a particle between wells in the
one-dimensional double-well potential with infinite high outside walls, based
on wave packet use and energy spectrum analysis, is presented. For the
double-well potential of the form in the external regions, an
exact analytical solution of the energy spectrum is found (by standard QM
approach), an analysis of oscillation periodicity is fulfilled, an approach for
exact analitical calculation of the oscillation period is proposed (for the
first time for the double-well potential).Comment: 11 pages, no figures. LaTeX 2e, class `elsart' (Elsevier Science) is
used. Reference correctio
Calculations of widths in the problem of decay by proton emission
We develop a new fully quantum method for determination of widths for nuclear
decay by proton emission where multiple internal reflections of wave packet
describing tunneling process inside proton--nucleus radial barrier are taken
into account. Exact solutions for amplitudes of wave function, penetrability
and reflection are found for -step barrier (at arbitrary ) which
approximates the realistic barrier. In contrast to semiclassical approach and
two-potential approach, we establish by this method essential dependence of the
penetrability on the starting point in the internal well where
proton starts to move outside (for example, for the
penetrability is changed up to 200 times; accuracy is ). We impose a new condition: in the beginning of the proton decay the
proton starts to move outside from minimum of the well. Such a condition
provides minimal calculated half-life and gives stable basis for predictions.
However, the half-lives calculated by such an approach turn out to be a little
closer to experimental data in comparison with the semiclassical half-lives.
Estimated influence of the external barrier region is up to 1.5 times for
changed penetrability.Comment: 14 pages, 4 figures eps; content is change
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