Explain vibration of a one dimensional mono atomic lattice and derive disperson relation
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The linear dispersion relation of a one-dimensional monatomic lattice with intersite interaction and nonlinear on-site potential. There is a lower cutoff mode q = 0 with the frequency ω = ω 1 and an upper cutoff mode q = π/a with the frequency ω = ω 2 = [ω 2 1 + 4k 2 /m] 1/2 .
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