Problem: Mass Defect

         Calculate the eigenfrequency of a linear chain with a mass defect (isotope) at position n=0, assuming a localized mode, described by

for the displacement of the nth atom, . The coupling between the atoms is represented by nearest-neighbor springs of spring constant (see Figure 2.2).

  
Figure 2.2: Linear chain of coupled atoms, with an isotope at the position n=0