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johnaphun
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Homework Statement
The model for the resistivity of metals can be described differently by adding the scattering term into the electron equation of motion.
mx'' + (2m/t)x' = qE
Where x is a mean quantity.
DC conductivity is found by considering the steady state when E is constant. Show that this results in the above equation leading to an equation for mean velocity of qEt/2m and that this equation in turn results in a more familiar equation of conductivity.
Now consider the case where an oscillating electric field is applied, by writing E as E^eiωt . Solve the equation of motion in this case and show that this leads to a complex AC conductivity varying with frequency as
s(w) = s(0)/1+iωt/ 2
The Attempt at a Solution
I'm ok with the first two parts of the question but I'm really stuck on the oscillating field bit, any help would be much appreciated!