I cannot see why the probaability ampltiude for an initial state to turn into another state is the inner product between the "another state" and the propogator acting on the initial state, since this is just equivalent to the inner product between the "another state" and the evolved initial state at the time of the evaluation.(adsbygoogle = window.adsbygoogle || []).push({});

For example, if I try it with the initial state as an energy eigenstate |1> and want to know the probability of it turning into a state |1>+|2> ( normalization constants implied), I would get a non zero result, but then that must be wrong because my initial state had zero probability of being in |2>. Thus my initial state should never be able to turn into |1>+|2>.

I can only see this working with eigenstates but not general ones, what am I missing?

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# Need help with transition amplitude

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