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Let's say I am supposed to animate the movement of some one-dimensional wavefunction as it hits a finite potential barrier like this:

I was supposed to know how to do this over a year ago, but I am never certain how to write the algorithm. What confuses me the most is how to show the incident wave "split into" the transmitted and reflected waves.

So, let's say I am given some wavefunction Ψ(x,t) that is moving towards a potential barrier or well. How should I write the algorithm? Is there some book you guys recommend that teaches this?

Also, I use Python. So, I would prefer any example code to be written in either Python or pseudocode. I do the plotting and animation with Scitools and Easyviz (I will take any recommendations if somebody recommend something else).