Quantum mechanics - question about the system

[paweld]

Let's asssume our system is in state $$|\psi\rangle$$. If we want to ask a true/false question about the system e.g. "Is the system in state $$|\phi \rangle$$?" does it always implay that after experiment which aims at answering this question the system will be in state $$|\phi \rangle$$. Could we answer this question and don't destroy the initial state (or destroy in another way).
Does it mean that during such experiment the state evolution is desciribe by the following projection operator: $$|\phi \rangle \langle \phi |\psi\rangle$$. Unfortunately this stae is unormallised. How we can describe the evolution of system during experiment by operator in Hilbert space.

 

[Gerenuk]

I'd also like to see how to interpret the measurement process as a normal quantum evolution.
https://www.physicsforums.com/showthread.php?t=349082

I looked through a lot of literature, but the only place I found such thing was a section in
http://www.amazon.com/dp/041512185X/?tag=pfamazon01-20
that said this is called or related to the Neumann interpretation. I don't know details though.