The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent, self-coherence length of propagating wave packets that obey the time-dependent Schr\"odinger equation and undergo a Goos-H\"anchen shift. In the Heisenberg limit they are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase {\Delta}{\phi} = 0.5 rad and shrink to particle-like dimensions for energy losses of more than 1000 eV.

中文翻译：

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波和粒子之间连续过渡的直接证据

通过使用电子显微镜测量渐逝场的离域来分析电子-物质相互作用的粒子和波描述之间的相关性。它的空间扩展与传播波包的能量相关、自相干长度相吻合，该波包遵循时间相关的薛定谔方程并经历古斯-H安陈位移。在海森堡极限中，它们是由相干非弹性库仑相互作用过程中的自干涉产生的，退相干相位 {\Delta}{\phi} = 0.5 rad，并收缩到类似粒子的尺寸，能量损失超过 1000 eV。