Rhett Allain shows you how to solve the standard 1D infinite square well problem using numerical method.
I know he is using this as a simple illustration, but it is more useful, especially to physics students, if he solves this for a finite square well.
But still, for the general public, this might be complicated enough. I wonder if someone with just computer coding but little physics can code this successfully. If you fall under this category, let me know how you did if you took up this task.