The Hamiltonian of the Interaction Between Electronic and Nuclear Subsystems of a Molecule

In this chapter, we focus on deriving the Hamiltonian governing the interaction between light and molecules, with a specific emphasis on Raman scattering. We simplify our analysis by considering a hydrogen molecule. To facilitate the separation of electron and nucleus movements, we employ the Born-Oppenheimer approximation. The central highlight of this chapter lies in the derivation of the Hamiltonian characterizing the electron-vibron interaction. This Hamiltonian assumes a form similar to the well-established Fröhlich Hamiltonian commonly used in solid-state physics, describing the interaction between electrons and phonons. Throughout the book, this interaction type takes center stage in elucidating various phenomena associated with Raman scattering.