Posted by Steve Simon on January 27, 2014, 7:27 pm, in reply to "Debye Heat Capacity"
Good question. But yes, I think you have missed something. From the way you state "one particle" and "the energy of one particle" in several places I think this is where the confusion lies. Let me see if I can clarify this.
(We will handle this issue later in the course as well when we study phonons, and potentially things will clarify even more then).
Einstein calculates the energy of a single Harmonic oscillator. In Plank's calculation each wave-mode in the box (each wavevector and polarization) should be treated as a separate harmonic oscillator. Even though a wave mode involves many atoms, the combined motion is treated as if it were a single harmonic oscillator. So, if we have N wave modes in the system, we sum the energy of these N harmonic oscillators.
Does this help?
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