  We slightly extend prior results about the derivation of the
Maxwell-Schr\"odinger equations from the bosonic Pauli-Fierz Hamiltonian. More
concretely, we show that the findings from [SIAM J. Math. Anal. 52(5),
4900-4936 (2020)] about the coherence of the quantized electromagnetic field
also hold for soft photons with small energies. This is achieved with the help
of an estimate from [arXiv:2202.05015] which proves that the domain of the
number of photon operator is invariant during the time evolution generated by
the Pauli-Fierz Hamiltonian.
