含时边界条件下薛定谔方程的非定域性和局域因果性
Nonlocality and local causality in the Schrödinger Equation with time-dependent boundary conditions
摘要：
我们研究了单个粒子在无限深阱中的非局域动力学。结果表明，在这种情况下，薛定谔方程（SE）违反了局部因果关系，导致瞬时变化的概率电流内的井内各处。这种违反是正式通过设计一个gedanken快于光的通信设备，它使用一个合奏的狭长腔和弱测量，以解决远离可移动的墙壁的动量的弱值。我们的系统是免费的，从通常的功能，造成非物理违反当地的因果关系时，使用（非相对论）SE，如瞬时变化的潜力或状态，涉及任意高的能量或速度。我们详细探讨了几种可能的文物，可以解释失败的SE尊重当地的因果关系，涉及时间依赖性边界条件的系统。
英文摘要：
We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitrarily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions.
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