Hi, I'm Aleks, a PhD student in quantum electronics.
I am working on quantum cascade lasers with rate equation model, for my masters I did modelling of QCL with transfer matrix method, I never used Levi, but I am more then capable or writing the solver for Schrodinger equation in any way you desire.
You haven't specified the length and details of the project, if you actually want to realize this structure, you probably need to model effects of doping, and then the solver for Poisson equation is needed, where the algorithm gets much complicated.
Since I have to do research for my own PhD please describe the project in more detail so I can estimate how much time I would need for it.
At this point I can modify my code to work with single quantum well and LHO potential in couple of days.