In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation valuethe 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. , where 0ˆz Ee z iq z z E e represents the dominant slow component of the radiation wave, and transverse field components, as well astransverse variation of the field are neglected. We examplify our modeling here for a case of Smith-Purcell radiation (see Fig. 1), for which the radiation wave is a Floquent mode: 4 zm iq z m m ze EEwith 0 2 zm z G q q m , G is the grating period, 0 Θ, / z q qcos q c and Θ is the incidence angle of the radiation wave relative to the axial interaction dimension. The radiation wave number z zm qq represents one of the space harmonics m that satisfies synchronizm condition with the electron [6]: 0 zm vq .We note that the analysis would be similar for the Cerenkov interaction scheme with Θ z q n cos , and () n the index of refraction of the medium. Furthermore, the analysis can be extended to the case of FEL and other interaction schemes [13,14].The solution of Schrodinger equation to zero order (i.e. free-space propagation) is well known. Assuming that the initial wavepacket, which is emitted at some point