I have been referring to QFT for the gifted amateur, p. 75. To evaluate whether a particle can exist beyond its forward light cone, we check if it has a non-zero amplitude. The amplitude being referred to is just its wave function, right? I am a little confused because we evaluate the following quantity: $$A = \langle x|e^{-i\hat{H}t}|x=0\rangle.\tag{8.16}$$ This looks like the expectation value of the time evolution operator between $x=0$ and some position, $x$.
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Qmechanic
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1Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Michael Seifert May 03 '22 at 13:52
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Why has the expectation value of time evolution operator been taken to denote the amplitude? – omnipotentcarrot05 May 03 '22 at 14:05
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1@omnipotentcarrot05 Related Question: https://physics.stackexchange.com/q/471572/ – Thatpotatoisaspy May 03 '22 at 14:46
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Amplitude $\langle x,t |x_0, t_0\rangle$ is probability amplitude from initial state $| x_0,t_0\rangle$ to final state $| x,t\rangle$, and its square represents probability. If we consider only positiom state as initial and final state, then time evolution factor is necessary. Now, $e^{-iHt} | x=0\rangle$ term is make sense.
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