In this diagram, we are shown a particle being trapped inside a piecewise potential well defined by the following function:
Where V??? is positive.
The question is, what are the possible energy eigenstates for a particle trapped inside this well?
In this post I would like to go through the standard solution for this problem using differential equations, and analyze the resulting non-analytical solution through a clever graphical approach. Additionally, I would like to end with plotting several possible eigenstates using Python.