Is conservation of energy, momentum, and other physical properties absolutely true in quantum mechanics, or only on average? As an example, think of a single particle in free space. Measure its energy, and write down the result. Then look at where it is, and measure the energy again. You'll probably get a different result the second time. I can see that the average of that distribution - at least in this case - is the original energy. This situation does not seem to mean too much though, since if you measure a particle it's not a closed system, so you don't expect energy to be conserved. Is there a more general statement of conservation of energy?