513.001 Molecular and Solid State Physics

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The relationship between phonons and photons

The propagation of low frequency (long wavelength) sound through a solid is described by the wave equation. The propagation of light through vacuum is also described by the wave equation. Since the same classical equation describes both photons and phonons, the calculation of the quantum states and the thermodynamic properites for phonons will be very similar to that for photons. The only real differences are that phonons travel at the speed of sound instead of the speed of light and there is one more possible polarization for sound waves than for light waves. Sound waves can have a polarized along the direction of propagation (longitudinal polarization) and there are two possible transverse polarizations. This makes the density of modes for phonons a factor of 3/2 greater than the density of modes for photons.

What is the equivalent of Planck's radiation law for phonons?

What is the specific heat of the phonons?