Wave packet motion in a quantized electromagnetic field: Analytic results

We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.