In the Sommerfeld Free Electron Model, electrons are treated as being free and independent as in the Drude's model. a) Mention the assumptions of the Sommerfeld free electron model. Elucidate the difference between classical free electron theory and quantum free electron theory. Describe how quantum free electron theory has been successful in overcoming the failures of classical free electron theory. b) What is the relation between n and kf in two dimensions? c) Prove that in two dimensions the free electron density of levels g() is a constant independent of for > 0, and 0 for < 0. What is the constant?