# Density of states

by kasse
Tags: density, states
 P: 463 1. The problem statement, all variables and given/known data We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by $$\psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L)$$ What is the density of states at the Fermi level for this metal? 3. The attempt at a solution The total energy of the system is $$E = \frac{\hbar^{2}\pi^{2}n^{2}}{2mL^{2}}$$ where n is the square of the sums of the three quantum numbers that determine each quantum state. At a certain energy all states up to $$E_{F}(0)=E_{0}n^{2}_{F}$$ is filled.