  We present a fully quantum model for the excitation of a bound electron based
on the free-electron bound-electron resonant interaction (FEBERI) scheme. The
bound electron is modeled as a quantum two-level system (TLS) at any initial
quantum (qubit) state, and the free electron is presented as a pre-shaped
quantum electron wavepacket (QEW). In the case that the QEW is short or
modulated at optical frequency, the TLS quantum state may be coherently
controlled with multiple modulation-correlated QEWs. For this case, we derive
the transition probability of the TLS due to interaction with a multi-particle
beam based on an analytical approximate solution of the Schrodinger equation
that amounts to using Born's probabilistic interpretation of the quantum
electron wavefunction. We verify the credibility of the analytical model at its
validity ranges using a fully quantum density matrix computation procedure. It
is shown that the transition probability can grow quadratically with the number
of correlated QEWs, and theoretically - exhibit full Rabi oscillation. The
study indicates a possibility of engineering the quantum state of a TLS by
utilizing a beam of shaped QEWs.
