Behavior of successive measurements

[mike1000]

[Mentors' note: Split off from this thread as it was a digression there]

You have a quantum state before a measurement: the state is evolving with time. A measurement changes the quantum state (to an eigenstate of the observable being measured); the new quantum state continues to evolve.

To what extent you can ask what is happening at the "instant of measurement" is a moot point.

After you make a measurement and find the particle to be in a particular eigenstate, if you measure that particle again will you find it to be in that same eigenstate?

 

[DrClaude]

After you make a measurement and find the particle to be in a particular eigenstate, if you measure that particle again will you find it to be in that same eigenstate?

Only if it is in an eigenstate of the Hamiltonian.

 

[Nugatory]

After you make a measurement and find the particle to be in a particular eigenstate, if you measure that particle again will you find it to be in that same eigenstate?

There's no way of knowing; measuring the particle again doesn't tell us anything about whether its state was an eigenstate of anything before we measured, it just gives us a measurement result. So the closest we can come to a sensible question might be something like "After you make a measurement and get the result corresponding to a particular eigenstate, if you measure that particle again will you get the same result?"

The answer to that question is "It depends".

The eigenstate in question is an eigenstate of some operator. What is that operator? Whatever it is, does it commute with the Hamiltonian? If so, the two measurements will be the same; if not, they may or may not be the same and the shorter the time interval between the two measurements, the more likely the two results will be the same.