Detector effect

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    WoutStoffels
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    When detecting through which of the two slits the electron went, we can differentiate between both slits, as opposed to the unobserved case. Therefore, the amplitude of the evolution between initial and final state is only determined by paths going through the one slit we observed. The interference term therefore disappears, and we see two lines corresponding to paths through each slit.

    In this case, the amplitude of an electron is simply given by A(x) = A1(x) or A2(x) depending on the slit, so the probability densities are given by A1² and A2².

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