# Phonon model

1. Nov 17, 2006

Let's suppose we have a Phonon gas in 1-D then:

- density of states $$g(k)=A/ \frac{ d\omega (k)}{dk}$$ (i don't remember the value of constant A sorry.. :tongue2: :tongue2: )

- The Schroedinguer equation (NO interaction) would be:

$$H_TOTAL =\Sum_{i}\frac{P^{2} _{i}}{2M}+ \sum_{i}B\omega ^{2}(k) (x_{i})^{2}$$

B is another constant..since the SE is separable we can find the exact solution in terms of Hermite Polynomials..my question is How i could get the density of states for this gas???

Ah..sorry another question if you know the "exact" partition function of a system can you determine the exact (by numercal or other methods) "shape" of the unit cell (i'm referring to get the sides of the unit cell, if this can be a cube or a parallepipede or other ..)