__1__.
Use a computer (Origin is best) to find and plot the bandstructure E(k) for
__bound__
solutions (E < 10eV) to the Kronig-Penney model using the
following parameters: V=10eV, a=0.4nm, and b=0.1nm. Start
by creating a column of energies (say, 0 to 10eV in 0.01eV
increments), converting these energies to Joules, and using the energies to
compute k1, α, and the LHS of
the K-P eqn. Then solve for k = arccos(LHS)/d.
Finally, plot E vs k. I __strongly__ advise doing all calculations in MKS units!

__2__.
How many bound bands are there? How does the bandwidth
change with energy? Is the change consistent with finite
lattice results? Explain.

__3__.
What is the energy (in eV) of the lowest allowed state?
What is the bandwidth of the lowest energy band? What is
the bandgap between the lowest two bands?

__4__.
Use numerical differentiation to find the effective mass of the
lowest energy states.