  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.
