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Given 1A.1 and 1A.2, I have been trying to apply the Schrödinger equation to reproduce 1A.3 and 1A.4 but have been struggling a bit. I was under the assumption that by applying ##\hat{W} \rvert {\psi} \rangle= i\hbar \frac {d}{dt} \rvert{\psi} \rangle## and then taking ##\langle{k'} \lvert \hat{W} \rvert{\psi} \rangle ## and ## \langle{i}\lvert \hat{W} \rvert{\psi} \rangle## would allow me to produce 1A.3 and 1A.4. I may very well be incorrect in my methods, but did the following rough calculation and got a very different result. (In my calculation, I assumed ## \hat{W} = H ##.)

Any clarification on how to reproduce 1A.3 and 1A.4 would be greatly appreciated.

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# I Schrödinger equation and interaction Hamiltonian

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