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Here is the part that is bothering me: enter image description here

Yeah, already here? So, my question: In the first line we have int picture states at time zero and in the second line we have limit of time evolv operator with the states in the int picture. How can we go from first to second line? Could we say that U operator evolves psi state to plus inf and then we make inner product with phi state? If this is so, are we saying that the amplitude is time independent?

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