Asymptotic behaviour of Bohmian trajectories in scattering situations
Sarah Römer, D. Dürr, T. Moser
We study the asymptotic behaviour of Bohmian trajectories in a scattering situation with short-range potential V and for wavefunctions with a scattering and a bound part. It is shown that the set of possible trajectories splits into trajectories whose long-time behaviour is governed by the scattering part of the wavefunction (scattering trajectories) and trajectories whose long time behaviour is governed by the bound part of the wavefunction (bound trajectories). Furthermore, the scattering trajectories behave like trajectories in classical mechanics in the limit t → ∞. As an intermediate step, we show that the asymptotic velocity exists almost surely and is randomly distributed with the density , where is the outgoing asymptote of the scattering part of the wavefunction.
arXiv:math-ph/0505074•Journal of Physics A Mathematical and General•Sep 14, 2005•7 citations