Hi all, I'm having some difficulty in my advanced QM class with adiabatic perturbations and Fermi's Golden Rule. I understand the physical reasons behind the conclusion of the adiabatic perturbation calculation (that a particle in the ground state will end up in the new Hamiltonian's ground state if you turn on perturbation veeeeeery slowly), but I don't follow the nitty-gritty calculation details. I'm even more lost on Fermi's golden rule. I won't bother with the homework questions that are giving me trouble just yet, since I don't understand the theory well enough yet to even make an attempt at it. Instead, do you have any useful resources you can suggest? A favourite textbook, maybe, or some course notes? I've spent a fair amount of time on Google, and nothing I've found has cleared up my confusion yet. There is one specific question I can ask about the golden rule, though: why do you take the time derivative of the transition probability to get the "transition rate"? That would make sense if you were taking the derivative of a function that gave the cumulative number of transitions that had occurred, but the transition probability is just that—a probability. If the probability were constant, you would still have transitions taking place at a fixed rate, but the derivative is 0. And, again, any favourite resources you could point me to would be greatly appreciated.