Having trouble with Density of States

[Dr Librarian]

I need to find the total number of states in a 1D monatomic lattice using the density of state equation g(ω), and I am having a hard time doing so. I'm fairly certain all I need to do ins integrate it, but this is proving to be a greater challenge than I thought it would. g(ω)=2L/(πaω_m)*sec(qa/2). I'm almost positive if I integrate from 0 to ω_m in terms of q, I will find the solution. However, every time I try, I get some crazy answer. what am I doing wrong?

 

[BigJDubs]

The first step is to determine the integration limits. Since the density of states equation is a function of angular frequency, ω, you will need to integrate over all possible values of this variable. Depending on the specific parameters given in your equation, this could range from 0 to infinity or from 0 to some upper bound. Once you have determined the integration limits, you can then evaluate the integral. Note that in order to solve the integral, you may need to use the substitution rule and/or partial fractions. After you have evaluated the integral, you will obtain the total number of states in the 1D monatomic lattice.