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A remark on the attainable set of the Schrödinger equation
Evolution Equations and Control Theory ( IF 1.3 ) Pub Date : 2020-06-12 , DOI: 10.3934/eect.2020075
Jonas Lampart ,

We discuss the set of wavefunctions $ \psi_V(t) $ that can be obtained from a given initial condition $ \psi_0 $ by applying the flow of the Schrödinger operator $ -\Delta + V(t,x) $ and varying the potential $ V(t,x) $. We show that this set has empty interior, both as a subset of the sphere in $ L^2( \mathbb{R}^d) $ and as a set of trajectories.

中文翻译:

关于薛定谔方程的可达到集的一个注记

我们讨论通过应用薛定ding算子$-\ Delta + V(t,x)$的流量并改变电势可以从给定的初始条件$ \ psi_0 $获得的一组波函数$ \ psi_V(t)$ $ V(t,x) $。我们证明该集合具有空的内部,既作为 $ L^2( \mathbb{R}^d) $ 中球体的子集,也作为一组轨迹。
更新日期:2020-06-12
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