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.

 

[Entropia]

I can provide some insight into these questions about quantum mechanics.

Firstly, the answer to the true/false question about the state of the system, such as "Is the system in state |\phi \rangle ?", depends on the experimental setup and the measurement process. In quantum mechanics, a measurement on a system can change its state, so it is not always the case that the system will end up in the state |\phi \rangle after the experiment. This is known as the measurement problem in quantum mechanics, and it is still an area of active research.

Secondly, it is possible to design an experiment that does not destroy the initial state of the system. This is known as a non-destructive measurement, and it can be achieved by carefully choosing the measurement apparatus and the interaction between the system and the apparatus. However, even in non-destructive measurements, the state of the system can still be affected.

Lastly, the evolution of the system during the experiment can be described by a projection operator, as you mentioned. However, it is important to note that the state |\phi \rangle \langle \phi| is not always the projection operator that describes the evolution of the system. It depends on the specific measurement being performed and the initial state of the system. In general, the evolution of the system during the experiment can be described by a unitary operator in Hilbert space, which preserves the norm of the state vector.

In summary, the true/false question about the state of the system in quantum mechanics is a complex issue and depends on the experimental setup and the measurement process. Non-destructive measurements are possible, but the state of the system can still be affected. The evolution of the system during the experiment can be described by a unitary operator in Hilbert space, which preserves the norm of the state vector.