散射情形下Bohmian轨线的渐近行为
Asymptotic Behavior of Bohmian Trajectories in Scattering Situations
摘要：
本文研究了具有短程势的散射情形下以及具有散射和束缚部分的波函数的玻姆轨线的渐近行为。它示出的一组可能的轨迹分裂成轨迹，其长时间的行为是由散射部分的波函数（散射轨迹）和轨迹，其长时间的行为是由约束部分的波函数（绑定轨迹）。此外，在长时间限制下，散射轨迹的行为类似于经典力学中的轨迹。作为中间步骤，我们证明了渐近速度v_{infty}：= lim_{t to infty} Q/t几乎必然存在，并且随密度随机分布|hat{Psi}^{out}|其中Psi^{out}是波函数散射部分的输出渐近线。
英文摘要：
We study the asymptotic behavior of Bohmian trajectories in a scattering situation with short range potential and for wave functions with a scattering and a bound part. It is shown that the set of possible trajectories splits into trajectories whose long time behavior is governed by the scattering part of the wave function (scattering trajectories) and trajectories whose long time behavior is governed by the bound part of the wave function (bound trajectories). Furthermore the scattering trajectories behave like trajectories in classical mechanics in the long time limit. As an intermediate step we show that the asymptotic velocity v_{infty}:=lim_{t to infty}Q/t exists almost surely and is randomly distributed with the density |hat{Psi}^{out}|^2, where Psi^{out} is the outgoing asymptote of the scattering part of the wave function.
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