# Chain of atoms in 1D

1. Nov 30, 2015

### Eats Dirt

1. The problem statement, all variables and given/known data
The system is a chain of atoms in 1D length L and number of atoms N. and
$$\epsilon_k=\hbar c_s k$$
a) What is the density of states?
b)The number of states that can be occupied (use boundary conditions)
c) Determine w_d(I think this is the debye frequency) in terms of N,L,k

3. The attempt at a solution
A. For the density of states I determined dk/(2pi) then changed variables to energy.
$$\frac{1}{c_s\hbar 2\pi}$$

B. From the state density using boundary conditions I really don't have a good idea of how to find the number of occupied states. I think I should start with my solution from part A but I can't seem to make the connection between the physical boundary conditions and occupation.

C. Again I am quite stuck

2. Dec 5, 2015