Free Electron Gas and the Jellium Model

The simplest approach is to describe the valence electrons in the solid as a free noninteracting electron gas in a box with the volume V, as we did in Chapter 3. We have to find the ground state for the Schrodinger equation 

The electrons must fulfill the Pauli principle and the wave function must be zero at the walls of the box with length I = resulting in the following values of the k 

The corresponding energy eigen values to this problem are 

To find the density of states per energy n(e) we start from  

The hypothetical metal jellium consists of an ordered array of positively charged metal ions surrounded by a structureless sea of electrons that behaves as a free electron gas (Fig. 6.13). 

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