Problem: Infinite-Dimensional DOS

   

Figure 4.4 shows the DOS for tight-binding electron bands in d= 1, 2, 3, and 4 dimensions. The bandwidth is normalized to 1. What is the DOS for ?

  
Figure 4.4: Density of states in the tight-binding approximation for dimensionality d=1,2,3, and 4. The energy scale is normalized to the bandwidth, and the DOS is normalized so that the integral under the curves is equal.