Tight-Binding

The Tight Binding (TB) approach consists of 1. an assumption, and 2. a procedure.

The assumption is that the

TB Hamiltonians are usually interpreted as having an electron tunneling or hopping between atoms, since going from an occupied to an unoccupied site should lower its energy (there is more space available). The energy change in tunneling from \(n\rightarrow m\) is \(-t_{nm}\),

\[ \hat{H}=\sum_n\epsilon_n\ket{n}\bra{n} \]