Green’s Functions for Tight-Binding Hamiltonians

Abstract

We introduce the so-called tight-binding Hamiltonians (TBH), which have the form where each state ∣ι〉 is an atomiclike orbital centered at the site ι; the sites {ι} form a lattice. Such Hamiltonians are very important in solid-state physics. Here we calculate the Green’s functions associated with the TBH for various simple lattices. We also review briefly some applications in solid-state physics.