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I am a little bit confused about the impulse response of one electron.

Assume that we have LTI system characterized by impulse response h(t) with unit gain, int{h(t)} = 1.

Let the input is current i(t) [Amp]. So the output current will be i(t)*h(t). We can view it as i(t) is dispersed in time due to passing through system h(t).

- If the current is only one electron with charge q and enters at time t = 0. Therefore i(t) = q delta(t).

- Therefore the output current is i(t)*h(t) = q.h(t)

The question is how one electron is dispersed in time.