论文标题
带圆锥衰减的Schrödinger操作员的散射
Scattering for Schrödinger operators with conical decay
论文作者
论文摘要
我们研究了Schrödinger运营商的散射特性，其潜力沿着$ \ bbr^d $的一系列光线散发出短距离。这概括了短距离散射的经典设置，其中假定电势沿\ emph {ash ash Rays衰减。对于这些操作员，我们表明，任何状态都将渐近不含的作品分解为可能与潜力相互作用的作品。我们从动力学和相应的补体描述方面给出了散射状态的微局部表征。我们还表明，在某些情况下，这些特征可能纯粹是空间的。
We study the scattering properties of Schrödinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along \emph{all} rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece which may interact with the potential for long times. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial.
