  Free-Electron Bound-Electron Resonant Interaction (FEBERI) is the resonant
inelastic interaction of periodically density-bunched free electrons with a
quantum two level system. We present a comprehensive relativistic quantum
mechanical theory for this interaction in a model in which the electrons are
represented as quantum electron wavepackets (QEW). The analysis reveals the
wave-particle duality nature of the QEW, delineating the point-particle-like
and wave-like interaction regimes, and manifesting the physical reality of the
wavefunction dimensions and its density modulation characteristics in
interaction with matter. The analysis comprehends the case of
laser-beam-modulated multiple QEWs that are modulation-phase correlated. Based
on the Born interpretation of the electron wavefunction we predict quantum
transitions enhancement proportional to the number of electrons squared,
analogous to superradiance.
