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：

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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。