Effects of the electron-hole interaction on the optical properties of materials: the Bethe-Salpeter equation

In these notes, the two-particle Hamiltonian for electron–hole interaction is derived. First, a simple Hartree–Fock based approach is used and an effective two-particle Schrödinger equation is obtained. Then, using Green's function techniques of many-body perturbation theory, correlation effects are introduced and the Bethe–Salpeter equation is deduced, where the electron–hole interaction is partially screened. Finally, some significant results in the literature are discussed.