Homework Help: 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

Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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