# Dimension-Dependent Stimulated Radiative Interaction of a Single Electron Quantum Wavepacket. (arXiv:1702.06394v4 [quant-ph] UPDATED)

In the foundation of quantum mechanics, the spatial dimensions of electron

wavepacket are understood only in terms of an expectation value - the

probability distribution of the particle location. One can still inquire how

the quantum electron wavepacket size affects a physical process. Here we

address the fundamental physics problem of particle-wave duality and the

measurability of a free electron quantum wavepacket. Our analysis of stimulated

radiative interaction of an electron wavepacket, accompanied by numerical

computations, reveals two limits. In the quantum regime of long wavepacket size

relative to radiation wavelength, one obtains only quantum-recoil multiphoton

sidebands in the electron energy spectrum. In the opposite regime, the

wavepacket interaction approaches the limit of classical point-particle

acceleration. The wavepacket features can be revealed in experiments carried

out in the intermediate regime of wavepacket size commensurate with the

radiation wavelength.