Forgive me for lack of formality and possibly incorrect understanding, but hopefully someone can both help to explain the intuition and also add mathematical formalism.
In classical electrodynamics, absorption of electromagnetic radiation by a solid, for example a collection of classical dipoles, may be thought of as a destructive interference effect. Oscillating light that is incident on a dielectric material will cause out of phase oscillation of the charges in the material, which will in turn radiate more electromagnetic fields. The incident and radiated fields conspire at lowest order to provide the exponential decay of the Beer-Lambert law. Note that this is an interference effect that relies on the addition of fields.
Now in quantum electrodynamics, where we consider a quantum system interacting with the quantized electromagnetic field, absorption can be considered rather to be a multiplicative effect, whereby the quantum state is multiplied by an annihilation operator which removes one quantum from the electromagnetic field.
Can someone help me rationalize the difference? I’m puzzled that quantum absorption seems to rely on “multiplicative interference” rather than “additive interference?” Thanks!