Hello, As a concrete model to refer to, I'll work with the one-particle system in a potential box with infinite edges. Inside the box is a potential barrier of height V. Let's say we've measured the energy at one moment to be E < V. The probability of measuring the particle inside the barrier is not zero. Say we measure it there, then [itex]E \geq V[/itex] and energy has changed as we would indeed expect from the fact that the Hamiltonian and position operator do not commute. Now my question is: why/how does the energy change when I perform a position measurement? I realize it is dangerous to ask such a question, because the mathematics doesn't give reasons or mechanisms. I suppose my question is: doesn't it? Am I right in supposing that the isolated system of, well, the described system together with the measuring apparatus has a total conserved energy? If so, the energy that the (sub)system gains when being seen inside the potential barrier, must've come from the measuring apparatus. So is it true that if we accept the mathematical formalism of QM, we must also accept that whenever I succesfully measure such a particle in the potential barrier, the measuring apparatus must be built so such that it will impart to it an amount of energy which is at least as great as how much the particle previously lacked to go over it? --- Another experiment: take the diffraction of a wave packet through a slate with a slit in it. Say the initial state is a plane wave approaching from the far left (with a known impulse), and say the final state is a position measurement on the far right. Consistent with the idea of diffraction, the momentum will most likely have changed from beginning till end. Can I regard the reason for this being that the slate in the middle can be see as a delta function-esque potential, that interacted with the particle (better: wave packet?) as to change its momentum? Or is this a fishy way of looking at things? Also, will the interaction of the particle with the wall/potential also be able to modify the particle's energy from beginning to end, or can it be assumed constant?