Measurement and expectation value

[hokhani]

TL;DR

Does a measurement affect the expectation value?

If measurement of an observable $\hat{A}$ is done over an ensembles of large number of copies of the system, then the average value of these measurements gives $\langle A \rangle$. If we do this measurement over this ensemble again, we expect to get to the last result $\langle A \rangle$. So, it seems that consequent measurements disturb the time dependency of $\langle A \rangle$. Doesn't it?

 

[anuttarasammyak]

TL;DR: Does a measurement affect the expectation value?

If we do this measurement over this ensemble again, we expect to get to the last result

I do not think so in general. Some counter examples.
Photons disappear on the screen in double slit experiment. We cannot repeat the experiment on the same photons.
Measurement of particle momentum by scattering ends to scattered states which does not hold the property of measured state.
In another thread of you, it was mentioned that in loose
position observation center of dispersing Gaussian packet does inertial motion in general so <x> changes with time.

You may be right on energy eigenstates for energy measurement.

 

[Roberto Pavani]

Do you mean repeating the measurement on a freshly prepared ensemble, or on the same ensemble after the first measurement? The answer is different in the two cases.

 

[hokhani]

Do you mean repeating the measurement on a freshly prepared ensemble, or on the same ensemble after the first measurement? The answer is different in the two cases.

On the same ensemble after the first measurement.

 

[Roberto Pavani]

The answer may also depend on how invasive the measurement is.
Some measurements strongly disturb the system (or even destroy it), while others can have a much smaller back-action.
I'm not sure that "measuring the same ensemble again" has a unique answer without specifying the measurement model.

I'm sure that some expert here can provide a better answer.