# Home Work #1 (Warm up)

*Due 5pm on Friday Week 1*

## Sommerfield model

**a)** Assuming the Sommerfield model, and starting from a sketch of allowed travelling 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 travelling 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.