1. << Fourier Transform of a Gaussian | Fourier Transforms and Wave Packets |
Find the Fourier transform of the (simplified) Gaussian function \begin{equation} f(x)=e^{-x^2} \end{equation} You may want to use the value of the following integral \begin{equation} \int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi} \end{equation}