Abstract This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum mechanics where the physical basis for single-valuedness has been questioned. It first constructs a large class of multi-valued wave functions based on knotted vortex filaments familiar in fluid mechanics, and then it argues that for free particles, these systems will likely radiate electromagnetic radiation if they are charged or have multipolar moments, and only if they are single-valued will they definitely be radiationless. Thus, it is proposed that electromagnetic radiation is possibly the mechanism that causes quantum wave functions to relax to states of single-valuedness, and that multi-valued states might possibly exist in nature for transient periods of time. If true, this would be a modification to the standard quantum mechanical formalism. A prediction is made that electrons in vector Aharonov-Bohm experiments should radiate energy at a rate dependent on the solenoid's magnetic flux.

中文翻译：

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薛定谔方程和辐射的多值涡旋解

摘要 本文解决了量子波函数在空间坐标中解析连续时的单值要求。这与德布罗意-玻姆、流体动力学或量子力学的随机模型特别相关，其中单值的物理基础受到质疑。它首先基于流体力学中熟悉的打结涡旋细丝构造了一大类多值波函数，然后认为对于自由粒子，如果这些系统带电或具有多极矩，则这些系统可能会辐射电磁辐射，并且仅当它们是单值的，它们肯定是无辐射的。因此，提出电磁辐射可能是导致量子波函数弛豫到单值状态的机制，并且多值状态可能在自然界中存在短暂的时间。如果为真，这将是对标准量子力学形式主义的修改。预测矢量 Aharonov-Bohm 实验中的电子应该以取决于螺线管磁通量的速率辐射能量。