Distinct one-particle states in a metal

[Niles]

Hi

In my book (Marder) it says that "There is no upper limit to the number of distinct one-particle electronic states that can inhabit a lattice, and there is no limit to the number of energy bands that the states can fill".

The latter statement I understand: That is obvious by looking at the reduced zone scheme. But the first statement I don't understand: Because we know that the independent states in the first Brillouin zone are separated by 2π/L, and there is a finite amount, namely N (the number of primitive cells). Of course we could just add an arbitrary lattice vector to these k, but then the resulting k' is not distinct.

Can you explain what Marder means by the first statement?


Niles.

 

[BigJDubs]

Marder's statement is referring to the fact that there is a continuous range of possible electronic states for a lattice, and no upper limit to the number of energy bands those states can fill. This means that the number of possible electronic states is not limited by the number of primitive cells in the lattice, but rather the energy levels that the electrons can fill. The continuous range of states is due to the fact that electrons can occupy any energy level within a given band, with the number of possible energy levels determined by the density of states.