I am trying to solve the linear Schrödinger equation with fourier transform as follows.
Although analytically I was able to solve it and create the graphs I want. I have difficulty creating the corresponding graph when I solve the problem numerically. Can you explain me what is my mistake in the following code?
To draw the plot
Plot[Abs[u[x, t]]^2, {x, 0, 20}, PlotRange -> All]
you need to give a numerical value to t and v too.