513.001 Molecular and Solid State Physics | |
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Continuum wave equationThe equations for the displacement of atoms along a linear chain are, Here M is the mass of the atoms, and C is the force constant for nearest neighbor atoms. The spacing between nearest neighbor atoms is a. Show that for long wavelengths these equations can be approximated by the wave equation, where v is the velocity of sound. What is v in terms of M, C, and a? When the equations are quantized, each normal mode solution of the wave equation can have one of the energies given by the equation Here n is the number of phonons in that normal mode. The average value of n is given by the Bose-Einstein factor. How many phonons are there in the normal mode with λ = L/100 at temperature T? |