When discussing the Sommerfeld model in class, we focused mostly on the three-dimensional
case, and found that the density of electronic states is proportional to √E (i.e. it increases with
energy). However, lower dimensional structures also have important applications and an
understanding of their electronic density of states is (DOS) therefore very important.
A quantum wire is a very thin structure in which electrons are confined to move in one
dimension only. For example, carbon nanotubes often behave as quantum wires. By
following methods similar to what we did in class for the 3-D case, show that the DOS of
a 1 -D wire is proportional to 1√E,