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In the initial approach to conductivity by Drude in 1900, he assumed there was some charged species which behaved like a classical gas in a solid. How does this picture break down when we turn to a quantum description of electrons in a solid?
In 3D, phonons gave us a density of states that went up with frequency^2 but the DOS for electrons rises with E^1/2. What the source of this difference?
Within the free electron model, is there a bound to the allowed values of the wavevector k? (recall that for phonons, the wavevector had to be within the first BZ) Is this surprising or expected?
How about for the allowed values of energy? (Recall that phonons had a maximum energy)
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