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Main Question or Discussion Point
[SOLVED] Momentumspace detection of an Electron (EWP)
I know there have been plenty of questions about electrons, momentum, and wave packets recently  but my question is distinct (and comes with a picture!).
Question: If you ionize an atom and detect the resulting free electron wave packet, how should it appear in momentum space?
My understanding is that the spaciallylocalized electron wave packet (EWP) that is born during ionization will be of a Gaussian shape, due to:
[tex]\Psi(x,t) = \frac{1}{\sqrt{2 \pi \hbar}} \int^{+\infty}_{\infty}{\phi(p)e^{i(px  Et)/\hbar} dp[/tex]
and that it will spread as it moves away from the ion and towards the detector. But won't the detector still process it as either a delta function or a Gaussian (in position space)? And if so, why isn't the resulting detection in momentum space a Gaussian (the Fourier Transform)?
The picture below is of an EWP that was single photon ionized by an XUV attosecond pulse. It looks to me like a "Sinc" function, which means that in position space it would be a rectangular function. This is without scattering (off of the ion core). My question really is why does this picture look like this? Thanks!
I know there have been plenty of questions about electrons, momentum, and wave packets recently  but my question is distinct (and comes with a picture!).
Question: If you ionize an atom and detect the resulting free electron wave packet, how should it appear in momentum space?
My understanding is that the spaciallylocalized electron wave packet (EWP) that is born during ionization will be of a Gaussian shape, due to:
[tex]\Psi(x,t) = \frac{1}{\sqrt{2 \pi \hbar}} \int^{+\infty}_{\infty}{\phi(p)e^{i(px  Et)/\hbar} dp[/tex]
and that it will spread as it moves away from the ion and towards the detector. But won't the detector still process it as either a delta function or a Gaussian (in position space)? And if so, why isn't the resulting detection in momentum space a Gaussian (the Fourier Transform)?
The picture below is of an EWP that was single photon ionized by an XUV attosecond pulse. It looks to me like a "Sinc" function, which means that in position space it would be a rectangular function. This is without scattering (off of the ion core). My question really is why does this picture look like this? Thanks!
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