Problem: Tight-Binding Band in Two Dimensions

   Consider electrons on a two-dimensional square lattice in tight-binding approximation, .

  
Figure 3.2: First Brillouin zone.

(a) Plot a few constant energy lines on the plane.

(b) Show that most of the constant energy lines cross the Brillouin zone boundary at a right angle. 

(c) Sketch along the W-X line (shown in Figure 3.2).