513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
of Elements

      

Two dimensional square lattice

Consider the in-plane vibrations of a two-dimensional square lattice of identical atoms, and let uxl,m denote the x-displacement of the atom in the lth column and mth row and uyl,m denote the y-displacement. The mass of each atom is M, and C is the force constant for nearest neighbor atoms.

Calculate the dispersion relation and plot the density of states.