(a) Using Equations 5.66 and 5.70, show that the wave function for a particle in the periodic delta function potential can be written in the form
ψ(x)=C{sin(kx)+e−iqasin[k(a−x)]},(0≤x≤a).
(Don't bother to determine the normalization constant C.)
(b) At the top of a band, where z=jπ, (a) yields ψ(x)=0/0 (indeterminate). Find the correct wave function for this case. Note what happens to ψ at each delta function.