We can use time dependant perturbation theory (specifically Fermi's Golden Rule) to calculate the transition rate (probability of transition per unit time) from one energy eigenstate to another. However, it seems to me that a 'transition' from one state to another can only occur if the system is measured and happens to collapse onto the desired final state. If no measurement occurs, the state can never truly transition - it will simply be in a superposition of initial and final states.
What kind of measurement is taking place (what Hermitian operator are we considering)? How often is this measurement taking place? And if this measurement is taking place regularly, why do we never consider its effects on the dynamics, given that each measurement should collapse the state vector in some way? I suppose different experiments will involve measuring different things, but any example would be helpful.