Hello! I am reading this paper and in deriving equations 6/7 and 11/12 they claim to use second oder time dependent perturbation theory (TDPT) in order to get the correction to the energy levels. Can someone point me towards some reading about that? In the QM textbooks I used, for TDPT they just calculate the change in population as a function of time, but I have never seen a formula for the change in energy levels. I am able to derive 6/7 and 11/12 by applying a unitary transformation to the hamiltonian and working from there, but is there a simple formula to get these equations directly (similar to the energy formula for time independent perturbation theory)? Thank you!