Problem: Phonon Mode of Two-Dimensional System

  Let us consider a two-dimensional system with a single-phonon mode of dispersion relation  

 

The function given by Eq. 4.3 is shown in Figure 4.3.

  
Figure 4.3: Two-dimensional phonon dispersion given by Eq. 4.3.

Use a computer to calculate the DOS. Divide the valid range of and values into equal parts. Divide the energy range into equal parts. Count how many k states fall into a given energy interval, and make a histogram.

Using the same scales, also plot the appropriate Debye density of states.