I have a concern about having some wave function psi, that is originally a superposition of many eigenstates (energies). Traditionally, it is said that the square of the coefficient of each of the component eigenfunctions represents the probability of measuring this particular energy eigenstate. Once a measurement is done, the wavefunction is to collapse to one of these eigenstates. My concern: Does this mean that energy is somehow measured to an infinite precision? I know obviously position and momentum cannot have this happen since they are continuous observables. What if I'm not able to accurately measure the energy? Or is this somehow a picture of a measurement that is ideal? I feel like this would be prevented by quantum mechanics, but I don't necessarily see how, unlike momentum and position uncertainties, which result from the changing of wavefunctions. I've seen other places that apparently inaccurate measurements result in another superposition, with more weighting of the eigenfunctions close to the region measured. If so, why is it commonly stated that the coefficient squared is straight up the probability of measuring an eigenstate?