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I am looking for a realistic explanation of the double-slit experiment in terms of wave packets (instead of stationary waves). First of all this results in using the scattering cross section, i.e. the probability current (not the density). Then, I guess, there is a kind of time average. So one should end up with something like
j_\text{scatt}(x,t) \sim \text{Im}\psi^\ast\nabla\psi
calculated for a scattered wave packet
|\psi,t\rangle = U(t,t_0)\,|\psi,t_0\rangle
and an integration like
N(\Omega) \sim \int_{-T}^{+T}dt\,\int_\Omega d\Omega \, j_\text{scatt}(x,t)
to calculate the number of particles N detected in Omega on a spherical screen.
Is there a rigorous derivation of such an expression for wave packets using e.g. time-dependent scattering theory?
j_\text{scatt}(x,t) \sim \text{Im}\psi^\ast\nabla\psi
calculated for a scattered wave packet
|\psi,t\rangle = U(t,t_0)\,|\psi,t_0\rangle
and an integration like
N(\Omega) \sim \int_{-T}^{+T}dt\,\int_\Omega d\Omega \, j_\text{scatt}(x,t)
to calculate the number of particles N detected in Omega on a spherical screen.
Is there a rigorous derivation of such an expression for wave packets using e.g. time-dependent scattering theory?
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