So what? You can always expand any state in any arbitrary basis. In some cases, when the time-dependent perturbation is small, then the unperturbed eigenstates of H0 will be VERY good approximations to the actual eigenstates of the time-dependent Hamiltonian ... there will be small corrections...
Well, it was kind of implied in my post, since I suggested you expand in the basis of eigenstates of the Hamiltonian. So the \phi_{n}(x) are the eigenstates of whatever Hamiltonian you are using.
No .. you can't use the form of the wavefunction at a particular time on one side of the equation, and the general time-dependent form on the other. Solving this type of problem is not always possible to do analytically. One way to go about it is to expand the wavefunction in the eigenstates...
I don't understand your confusion ... how is that any different than the sum expression you posted earlier where only one coefficient is non-zero? In such a case, then there is only one time-dependent frequency, so there is no beating, and no modulation of the amplitude. There is just the...
No, that mathematical expression is always correct. Remember that the propagator is an operator, so in order to apply it, you need to pull it into the sum and apply it to each of the eigenstates. In such a case, you will get a *different* time-dependent phase factor for each term in the sum...
If you know the wavefunction at any point in time (which we will call t=0), and you know the Hamiltonian, then the expression (similar to what LostConjugate posted), \psi(x,t)=exp[-\frac{i\hat{H}t}{\hbar}]\psi(x,0) will give you the time-evolution of the wavefunction. The operator...
The time dependence is only a phase *if* you are dealing with an eigenstate of the Hamiltonian ... the amplitude will also be time-dependent if your wavefunction is a superposition state. However, the equation you gave in your first post is (almost) correct in either case. The only issue is...
Thanks! That looks like a very interesting article, but I am not sure how it gets at the measurement problem that we are discussing. Perhaps it will be more clear after I have had more time to read it carefully.
I agree .. that is exactly that I was saying (or at least trying to), back on the first page of this thread :wink:.
The interesting question raised by that is, why not? Is it due to some fundamental limitation (i.e. your last statement should be strengthened to "... axiom can't exist.")? Or...
This is an interesting point, but seems to employ the same vague definition for "measurement". Can you be a little more specific? What is the character of the momentum measurement that you are talking about? Does it involve a time-ordered sequence of position measurements, or something else...
While I understand your point, and tend to agree with it for my own personal purposes, there are entire branches of science where progress is made on a daily basis without any direct (or even indirect) consideration of philosophical issues. As I said above, I agree that our understanding of the...
I am aware that single-detector configurations can be used for MZ-interferometers for many applications, but it is so clear to me how such an interferometer can be used to analyze single photon experiments, where you need to have a result for every photon passing through the apparatus. You can...
I know you think that, but it is not correct. For example, how can mass-less particles like photons undergo collisions? Even for massive particles, you have BEC states that allow an arbitrary number of spin-zero bosons to populate the same quantum state. That is not quite the same thing as...
Yes you did, because you specified an MZ interferometer, which uses two detectors .. you can ignore one if you want, but then you are not really doing interferometry.
Please explain how you can make an MZ interferometer work in such a fashion. Remember an MZ interferometer is what *you*...
Your experiment is possible in principle, although as Mike H suggests, you might want to consider using universal indicator. Some other things you might also need to consider:
1) An indicator is itself a weak acid .. the color change(s) are induced by protonation/deprotonation reactions...