2. Using the Ziman model, the band gap was approximated by comparing the expectations of the potential energies for symmetric and antisymmetric wavefunctions. In class, the case of a relatively wide barrier was worked out, and the gap was found to rapidly decrease with increasing band number. Now consider a very narrow barrier. a. Approximately how narrow should the barrier be (compared to the well width) so that the band gap is nearly constant up to the 10th band? b. What should the barrier height be in this case so that the tunneling between wells is the same as for the wider band considered in class? c. Forthe barrier width and height computed above, approximately what is the band gap for the lowest band