If we integrate the probability of locating a system in a given state with respect to time, we arrive at Fermi's Golden Rule , a bread-and-butter expression which can describe some photophysical processes as some perturbation to the system. If we redefine our previous Hamiltonian (Equation ) as some base system H 0 with some small perturbations acting on it H x , we can expand our Hamiltonian with respect to a series of ordered terms: