This is a unit that introduces the Fourier transform and its properties and then applies the Fourier transform to free particle wave packets in non-relativistic quantum mechanics. The activities and homework are listed here. Appropriate text materials for mini-lectures can be found in the chapter Fourier Transforms and Wave Packets in the free online textbook The Geometry of Mathematical Methods.

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}

Students find a wavefunction that corresponds to a Gaussian probability density.

Students calculate the Fourier transform of the Dirac delta function.