Posted by Steve Simon on March 15, 2013, 11:16 am, in reply to "The Debye calculation"
The extra factor of three is out front. Each oscillator gets an energy hbar omega (n+1/2) where omega is the oscillator frequency. We just need to add up all the oscillation modes. For each wave vector k, in 3 dimensions there are three different oscillation modes - you can think of these as being the three directions of motion.. Or equivalently there is one longitudinal and two transverse modes at each k.
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