A standard problem in introductory quantum mechanics is to solve for the allowed bound state energies for a particle in a finite potential well. In the attached Jupyter Notebook, I describe this problem, and work out the numerical solutions, and display the results both graphically and numerically.

The code is easily modified for any finite well; shown in the notebook is the solution for an electron in a well with depth 80 eV and width 0.4 nm. You can find the Jupyter Notebook file (and the needed associated image file) at my Scipyscriptrepo GitHub site, or view the notebook using this nbviewer link.