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okaythanksbud

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From what I've read, every measurement of a system gives us values that are the eigenvalues of a certain hermitian operator, which "corresponds" to the measurement. This seems like it was pulled out of thin air but its clear enough so ill take it. Now onto the questions:

1: Is it true that upon measurement the wave function will collapse into the eigenvector/eigenfunction corresponding to the eigenvalue we measured. Does this mean, for example, that if I measured energy E_n in a particle in a box, the wave function from that point forward would definitely be the solution to Hf=E_nf? (H is the hamiltonian operator with a potential of 0, and f(0)=f(L)=0--I discounted the time factor since it only affects the solution up to a phase)

2: If I were to shake the box after this measurement, im assuming it would go back to square 1 of being in an indeterminate state (assuming in 1) the wave function collapses into a determined state corresponding to E_n). Does the initial measurement have any bearing on the system now?

3: just to be sure, does a state refer to every possible description of a particle in some instant or just one description? If I interpret this correctly, the wave function is supposed to hold all the information about the state of our system. Does this mean there is only one wave function (aka only one state--which is a superposition of other states) for our system, or is there one for every measurement we can make (i.e. would the wave function of an electron in a box allow us to also predict, say, the spin of it in addition to its position, though not necessarily both simultaneously? or is there another wave function for that)?

4: Are states ever related--can making a measurement on one ever tell us anything about the other? Im assuming the answer must be yes--if so how can we tell? Is this maybe related to the commutator?

5: is it possible to collapse the wave function into a new state that is not definite, but a new "truncated" one? For example, is it possible to make the deduction, say for a particle in a box, that the energy is NOT E_n, giving us a new wave function corresponding to the superposition of every state besides the one corresponding to E_n? I have no idea about this one, im tempted to say no since Im unsure it would be possible to find Fourier coefficients to match a certain initial condition.

6: if A is some operator corresponding to a measurement, does Af actually represent anything (where f is a wave function for the system)? It makes sense that it would be used to calculate expectation values and in the case of the hamiltonian solve for the wavefunction due to its relation with the time derivative, but does it represent anything physical in our system? Its not like Af is a description of the state of our system or anything, correct?

Im sorry if these questions were very stupid or made no sense, its very hard to tell what inferences I can/should be making at the moment since learning about this is making me feel like im learning arithmetic for the first time in my life. I would greatly appreciate any help.