We present a comprehensive relativistic quantum-mechanical theory for interaction of a free electron with a bound electron in a model, where the free electron is represented as a finite-size quantum electron wave packet (QEW) and the bound electron is modeled by a quantum two-level system (TLS). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wavelike interaction regimes and manifesting the physical reality of the wave function dimensions when interacting with matter. This QEW size dependence may be used for interrogation and coherent control of superposition states in a TLS and for enhancement of cathodoluminescence and electron energy-loss spectroscopy in electron microscopy.

中文翻译：

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自由电子-束缚电子相互作用中的量子波-粒子对偶性

我们提出了模型中自由电子与束缚电子相互作用的综合相对论量子力学理论，其中自由电子表示为有限尺寸的量子电子波包 (QEW)，束缚电子由量子建模两级系统 (TLS)。该分析揭示了 QEW 的波粒二象性，描绘了点粒子和波状相互作用机制，并体现了与物质相互作用时波函数维度的物理现实。这种 QEW 尺寸依赖性可用于 TLS 中叠加态的询问和相干控制，以及用于增强电子显微镜中的阴极发光和电子能量损失光谱。