# Singular behavior of the density state called a van Hove singularity

1. Mar 1, 2013

### JordanGo

1. The problem statement, all variables and given/known data

I was doing a condensed matter problem (3rd year) of a phonon dispersion relation for a monatomic linear chain. It asked told me to derive an expression for the density state per unit length and I obtained the following:
$g(\omega) = \frac{L}{a\p} \frac{1}{4C/M - \omega^{2}}$

2. Relevant equations

The singularity occurs at
$\omega = 2(\frac{C}{M})^{1/2}$

3. The attempt at a solution
Can someone explain the origin of this singularity?