Students use an applet to explore the role of the parameters \(N\), \(x_o\), and \(\sigma\) in the shape of a Gaussian \begin{equation} f(x)=Ne^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation}
1. << Fourier Transform of a Gaussian | Fourier Transforms and Wave Packets |
A Gaussian is a function of the form \begin{equation} f(x)=Ne^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation} Use the applet at Gaussians to explore the role of the parameters \(N\), \(x_o\), and \(\sigma\) in the shape of a Gaussian. Make sure that not only do you know the role of each parameter, but also that you can EXPLAIN this behaviour based on the algebraic expression for the Gaussian function.