- #1
happyparticle
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- TL;DR Summary
- Computing the Fourier transform of the density fluctuation.
There is a Fourier transform that I don't really understand in my textbook.
I have the following equation:
##\ddot{\delta} + 2H\dot{\delta} -\frac{3}{2} \Omega_m H^2 \delta = 0##
Then using the Fourier transform:
##\delta_{\vec{k}} = \frac{1}{V} \int \delta(\vec{r}) e^{i \vec{k} \cdot \vec{r}} d^3 r##
Where ##\delta(\vec{r})## is the density fluctuation.
We get
##\ddot{\delta_{\vec{k}}} + 2H\dot{\delta_{\vec{k}}} -\frac{3}{2} \Omega_m H^2 \delta_{\vec{k}} = 0##
The only function that does that is a gaussian function, I guess. I don't understand the process here.
Thank you
I have the following equation:
##\ddot{\delta} + 2H\dot{\delta} -\frac{3}{2} \Omega_m H^2 \delta = 0##
Then using the Fourier transform:
##\delta_{\vec{k}} = \frac{1}{V} \int \delta(\vec{r}) e^{i \vec{k} \cdot \vec{r}} d^3 r##
Where ##\delta(\vec{r})## is the density fluctuation.
We get
##\ddot{\delta_{\vec{k}}} + 2H\dot{\delta_{\vec{k}}} -\frac{3}{2} \Omega_m H^2 \delta_{\vec{k}} = 0##
The only function that does that is a gaussian function, I guess. I don't understand the process here.
Thank you