For Schrödinger equations with both time-independent and time-dependent Kato potentials, we give a simple proof of the maximal speed bound. The latter states that the probability to find the quantum system outside a ball of radius proportional to the time lapsed decays as an inverse power of time. We give an explicit expression for the constant of proportionality in terms of the maximal energy available to the initial condition. For the time-independent part of the interaction, we require neither decay at infinity nor smoothness.

中文翻译：

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量子传播的最大速度

对于具有与时间无关和与时间有关的Kato势的Schrödinger方程，我们给出了最大速度边界的简单证明。后者指出，在与所经过的时间成比例的半径的球外找到量子系统的概率会随着时间的倒数而衰减。我们根据初始条件可利用的最大能量给出了比例常数的显式表达式。对于交互作用的与时间无关的部分，我们既不需要无穷大的衰减，也不需要平滑度。