Yes.
OK. That is extremely interesting; There is a coefficient of each of the energy states -- say "a" and "b" which then are added as in: phi = a*S1 + b*S2; that determine the relative "amounts" of each state that an item is in. In none of my books is the "sampling" of a combined energy...
Good. That was bothering me -- for I know infinite energies are a problem in QCD, QED, with virtual photons (etc) and I wasn't sure if this was another instance of that just swept under the rug...
Let me restate that to see if I am understanding you:
Schrodinger's equation's solutions are...
I am having trouble understanding (not for homework) what a wave packet is in terms of the correspondence of the idea of a wave packet to a "point like" particle. I'd like to focus on the 1d wave packet ultimately, but in order to describe my consternation -- let me detour to a well defined...