  We study the photon emission rate of a non relativistic charged particle
interacting with an external classical noise through its position. Both the
particle and the electromagnetic field are quantized. Under only the dipole
approximation, the equations of motion can be solved exactly for a free
particle, or a particle bounded by an harmonic potential. The physical quantity
we will be interested in is the spectrum of the radiation emitted by the
particle, due to the interaction with the noise. We will highlight several
properties of the spectrum and clarify some issues appeared in the literature,
regarding the exact mathematical formula of a spectrum for a free particle.
