Q4: In a linear monoatomic chain of four atoms, the end atoms are fixed. Considering only the nearest neighbor interaction and assuming that the force between any two atoms is proportional to their relative displacement, set up the equation of motion for longitudinal vibrations of free atoms. Show that the frequencies of two normal modes are related as w² = 3w²
Q4: In a linear monoatomic chain of four atoms, the end atoms are fixed. Considering only the nearest neighbor interaction and assuming that the force between any two atoms is proportional to their relative displacement, set up the equation of motion for longitudinal vibrations of free atoms. Show that the frequencies of two normal modes are related as w² = 3w²
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Transcribed Image Text:Q4: In a linear monoatomic chain of four atoms, the end atoms are fixed. Considering only the nearest neighbor
interaction and assuming that the force between any two atoms is proportional to their relative displacement, set
up the equation of motion for longitudinal vibrations of free atoms. Show that the frequencies of two normal
modes are related as w² = 3w²
Q5: Prove that in a one dimensional diatomic lattice, the optical branch is given by;
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