When fixing a specific gauge, one defines the gaugedependent vector and scalar potentials for the electromagnetic field. By choosing the Coulomb Gauge (i.e. by enforcing ∇ • A = 0) which makes the vector po-tential purely transverse, Â = Â⊥ , the Hamiltonian of point charge particles (including both electrons and nuclei) interacting with the electromagnetic field can be written as follows Ĥ = N j 1 2m j pj -q j Â⊥ (r j ) 2 + ϵ 0 2 dr 3 Ê2 ∥ (r)