Recent content by hokhani

Ok, and I told since ##[H,\hat{A}=\hat{S_z}]=0##, in the Stern-Gerlach experiment after the time ##t_1## the system is always in the specific spin, say up, and this way my problem in post #13 is resolved. I hadn't considered there the commutation of ##[\hat{A} , H]=0##.

No, I approved your comment about S-G experiment by taking ##\hat{A}=\hat{S_z}## and ##A## in the Hamiltonian is not operator but the vector potential for magnetic field.

You are right, I edited the post #15.

Right, so for example in the S-G experiment, before the first measurement we have the Hamiltonian ##\frac{\hat{P}^2}{2m}##, at first measurement at ##t_1## we have Hamiltonian in the form ##\frac{(\hat{P}-eA/c)^2}{2m}+S_zB## and between ##t_1## and ##t_2## we have again ##\frac{\hat{P}^2}{2m}##...

Thank you and Matterwave. We are at a good point to review my problem again. We would like to measure the quantity ##\hat{A}## and ##[\hat{H}, \hat{A}]\ne0##. By the first measurement which is done at time ##t_1## the system collapses to one of the eigenfunctions of ##\hat{A}##, say...

And you reconciled very well the reason in the two models. Thanks.

Right, but by "classical reason" I meant how to explain the reality in the classical model.

You mean that if the second measurement is done long after the first one, the second result may be different. But I haven't seen anywhere that the time between the two consequent measurements of commuting operators matters. Could you please explain more?

So, we cannot consider the classical measurements like the expectation values in QM because we may have classical measurements which don't affect the system. But, from Ehrenfest theorem, we expect the wave pocket to behave like a classical particle!

Ok, but do you mean that charge acceleration doesn't generate radiation? Then, what is the classical reason of radiation?

From classical view, even in a stationary state of an atom electrons have acceleration and they must radiate.

As far as I know, in QM an alternating electric field sets Floquet levels with energy spacing ##\hbar \omega##. But I don't know what would happen for electron.

Right, there are experimental limitations, but I am looking to this subject in a pure theoretical view.

Exactly. My discussion is only in the framework of non-relativistic QM.

On the same ensemble after the first measurement.