Green’s Functions for Tight Binding Hamiltonians

Abstract

In this chapter we introduce the Tight Binding Hamiltonian (TBH)

$$ H = \sum\limits_{\underline \ell } {|\ell > \varepsilon \underline {_\ell } < \ell |} + \sum\limits_{\underline \ell \underline m } {|\ell > V_{\underline \ell \underline m } < m|} $$

((5.8))

where each state |l> is an atomic like orbital centered at the site l. The sites {l} form a regular lattice. The quantity ε _l is the energy of an electron located at the site l in the absence of V.. The quantity V _lm is the amplitude for transfering an electron from the site l to the site m. The electronic motion governed by the TBH (5.8) is mathematically equivalent to the motion of a coupled set of pendulums (see Table 5.1).