There is another topic for this but I didn't quite see it and I don't know how I've gone so far through my course not asking this simple question. So whats the difference? My thought process for hydrogen. I know it can have quantised values of energy, the energy values are the Eigen values of the wave state. There can be multiple Eigen values, E, with a corresponding wave states, Ψ. Which can be of the form HΨ=EΨ. If I want to find the expectation value, <H> this will give me the value of E that is most likely to be found every time I repeat a measurement on the system? The value I get for <H> will not change, but the value of E in the other equation can change. Is my thought process correct?