(a) Imagine that we have a two-dimensional free electron system. That is, there are N free electrons in a large square whose size is L L. Find the density of states, g(E).

(b) What are the Fermi energy (EF ) and total energy (ET ) in terms of N?

(c) Repeat (a) and (b) for a one-dimensional free electron system, i.e. N free electrons inside a large interval of length L. [5 pt] (d) What will g(E), EF and ET be if N free electrons are palced in an n-dimensional box with size L L L = L n (n 4)?

(d) What will g(E), EF and ET be if N free electrons are placed in an n-dimensional box with size L L L = L n (n 4)?