Students find a wavefunction that corresponds to a Gaussian probability density.
The Gaussian \begin{equation} {\cal P}(x)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation} is normalized so that the area under the curve is equal to one. If this Gaussian represents the probability density for a free quantum mechanical particle, what is a possible wavefunction?