Light-matter interactions are an outcome of an oscillating electromagnetic field resonantly interacting with charged particles. Molecular spectroscopy uses light to interrogate matter, but actually never see the molecules, only their influence on the light. Different types of spectroscopy give different perspectives. This indirect contact with the microscopic targets means the interpretation of spectroscopy requires a model, whether it's stated or not.
Modeling and laboratory practice of spectroscopy are hooked into each other, and spectroscopy is merely as useful as its ability to differentiate different models. This makes an accurate theoretical description of the underlying physical process governing the interaction of light and matter important.
Quantum mechanically, spectroscopy is a perturbation induced by the light which acts to couple quantum states of the charged particles in the matter. Hamiltonian for the light–matter interaction, which within the most general sense would be of the form
Quantum mechanical treatment of the light would explain the light in terms of photons for diverse modes of electromagnetic radiation. Light field described by a time-dependent vector potential acts on the matter, but the matter does not influence the light. In that case, HL can be ignored, and have Hamiltonian for the system is