(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am so confused about propagators:

[tex]K(x,t;x',0) = \int |E\rangle e^{-iEt/\hbar} \langle E| dE[/tex]

I understand the RHS of that equation perfectly: it just decomposes the time-independent state into its eigenstates and then propagates each of the eigenstates individually.

I would understand the LHS if and only if the ";x'," were removed from it. I simply do not understand why you need to get rid of the prime after you propagate the state? Why can you not propagate a time-independent wave-function of x' and get a time-independent wavefunction of x not x'?

EDIT: here is another equation from the wikipedia site on propagators:

[tex]\psi(x,t) = \int_{-\infty}^\infty \psi(x',0) K(x,t; x', 0) dx'[/tex]

I think I am starting to understand this better. So, the reason you have an x and an x' is that the x' is summed over (continuously) if we want to think of the propagator just as a huge summation. But still why don't other operators like the Hamiltonian have an (x,x') attached to them? You can think of the Hamiltonian as a matrix operator as well.

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Propagators homework

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