Due 5pm on Friday Week 1

a) Assuming the Sommerfeld model, and starting from a sketch of allowed traveling wave states in k-space, show that n_3d = (k_F)³/3π².

b) Do the same thing for a one-dimensional electron gas, i.e. relate n_1d to k_F (now the electron traveling waves are described by only k_x).

c) Estimate n_3d and E_F for gold using physical/chemical parameters such as density and electron configuration.

• Ashcroft & Mermin - 2-d problem