I read your hint in the other thread. Then what I've just put here is right, isn't it? I put the state straightforward in the momentum basis just by introducing the closure relation for the |p> basis into the |r0> state...
I must write the state of a free particle with well determined position (r0) at t=0. I assume that, as it has well-determined position, it's an eigenstate of position operator, with eigenvalue r0. So is this it, in the momentum basis?
\mid \psi (t_{0})\rangle = \mid...
I think DrDu is right, when you integrate you are sort of adding hamiltonians at different t's, and then the exponential form doesn't hold anymore unless they all commute.
No, of course you can't because the product of exponentials of two operators can't be written as the exponential of the sum unless the operators commute!
Thank you!
The time evolution operaton may be written formally as:
This is an actual solution to:
only in the case that [H(t1),H(t2)]=0 (that is: the hamiltonian commutes in different instants of time) Of course, this includes the case of a time independent hamiltonian.
If this is not the case, the...
If we know exactly the position of the particle at t=0, does this mean that at this time its state is an eigenstate of position, with eigenvalue r0? How can I put that into:
http://upload.wikimedia.org/math/1/0/3/10317da44bf13fbd709cd642c5143b9f.png
Should I just skip Dirac notation and...
The question is: what is the quantum state of a free particle t time after its detection at the position r0 in t=0?
I know I have to use the evolution operator with the hamiltonian of a free particle. My actual problem is more stupid than that: I don't really know how to express the STATE of...