I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform?) on them. So I have the wave functions ($\Psi$, $1\times N$ vectors), and the continuous equation:

$$\zeta(x)=\int \mathrm{d} x' g_{\sigma_x}\left(x-x'\right)\left|\Psi(x')\right|^2,$$ where $\zeta(x)$ is a $1\times N$ vector too, and $g_{\sigma_x}$ is normal distribution.

I do not know, hot to do this with discrete vectors in MATLAB. I did not find any functions or algorithms.


closed as off-topic by Kyle Kanos, Thomas Fritsch, Jon Custer, John Rennie, Chris Jun 5 at 8:26

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  • $\begingroup$ Pretty sure MATLAB has a convolution function. Search for that. $\endgroup$ – Gilbert Jun 3 at 2:09
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    $\begingroup$ I'm voting to close this question as off-topic because it's about using a particular software and not physics. $\endgroup$ – Kyle Kanos Jun 3 at 11:32
  • $\begingroup$ Cross posted here. $\endgroup$ – Chris Jun 5 at 8:27