In talking about Raman spectroscopy, one finds the Stokes line is simply the difference between the energy of an incoming photon and an emitted photon. This energy corresponds to a vibrational transition in terms of energy. Yet, the light sent at the molecule is usually much higher energy than that vibrational transition (or else we would just be doing IR).
The explanation I've heard is that the state which holds all that energy in between the ground vibrational state and decaying back to the first vibrationally excited state is a virtual state.
From doing some reading, I have gathered that a virtual state is called virtual not because it's imaginary, but because it's not an eigenfunction of the hamiltonian of the system.
Where does this state come from? I've heard that it drops out of some perturbation theory. Because Raman is intricately connected with polarizabilities, I imagine this might be perturbations to the time-dependent Schroedinger equation.
So, to put some actual questions out there:
What is meant by "virtual state"? In what sense is it virtual?
Can anyone show me the perturbation theory where this comes from? Even if it is just a reference, that would be greatly appreciated.
I have also seen this is somehow connected with Feshbach Resonance which I know nothing about, so an answer which addresses that point would be a good one.