Electronic Wave Packet in a Quantized Electromagnetic Field

We study a non-stationary electronic wave packet in a quantized
electromagnetic field. Generally, the electron and field become
entangled as the electronic wave packet evolves. Here we find that, when the initial photon state is a coherent one, the wavefunction of the system can be factorized if we neglect the transferred photon number. In this case, the quantized-field calculation is equivalent to the semi-classical calculation.