# Hamiltonian of a metal lattice

1. Feb 2, 2010

### Niles

Hi guys

I have the Hamiltonian, which describes my lattice of NxN metal atoms, and their mutual coupling. What I need is the density of states of this lattice, and I am quite sure that there is a way to find it from my Hamiltonian; I just need to find out how.

What I thought was that I can of course find the eigenenergies and corresponding eigenvectors from my Hamiltonian. In order to find the DOS I assume I need to find an expression relating the eigenenergies and the number of possible states. Am I way off here?

2. Feb 5, 2010

### turin

Your idea sounds correct. I am not the best at solid state (that's what you're doing, right?), but since no one else is chiming in ...

Can you write your Hamiltonian for us? Specifically, what kind of interaction are you talking about? If I remember correctly from solid state class, you typically approximate the potential as a sum of terms proportional to (xa2-xb2), xa and xb being the positions of some (nearest neighbor?) atoms, and if you go to reciprocal space, the reciprocal volume of the (Brillouin?) zones give you the density of states (in energy). (Is that because it is approximately linear?)

I don't know what to do if you consider higher-order details of the interaction potential (I've only taken one solid state class, and solid state is not my field of study). I'll think about it some more.