Waves in a One-dimensional Diatomic Crystal

—Arrangement of atoms in one-dimensional diatomic molecular lattice. 

To solve Eq. (2.1), we assume sinusoidal standing waves for both types of atoms, but with different phases  

If our assumptions (2.2) are to furnish solutions of Eq. (2.1), we must have Eqs. (2.4) satisfied independent of j that is, for each atom in tho chain. The only way to do this is for each of the four coefficients of sin 

Thus we should not expect to find solutions for our equations, since there are more equations than unknowns, but it turns out that the equations are just so set up that they have solutions. We have the four equations 

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