超振荡和超位移的薛定谔演化的统一方法
A unified approach to Schrödinger evolution of superoscillations and supershifts
摘要：
超振荡函数和超位移在物理学的弱测量中自然出现。它们作为不定常薛定谔方程的初始条件的演化是量子力学和数学分析中的一个重要而具有挑战性的问题。在演化过程中编码超振荡持续性的概念是解的（更一般的）超移位性质。本文给出了确定不定常薛定谔方程解的超移性质的统一方法。我们的结果的主要优点和新颖性是，他们只需要适当的估计和正则性的假设上的格林函数，而不是其明确的形式。有了这种有效的一般技术，我们能够处理各种潜力。
英文摘要：
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper we give a unified approach to determine the supershift property for the solution of the time dependent Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green's function, but not its explicit form. With this efficient general technique we are able to treat various potentials.
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