An effective Hamiltonian and time-independent perturbation theory

Using a formalism set up by Bloch an effective Hamiltonian is introduced which, when expanded in powers of a perturbation V, generalizes the Rayleigh-Schrödinger perturbation theory. This effective Hamiltonian provides a simple way of handling degeneracies and the orthonormalization of the perturbed wave functions. As an illustration the spin Hamiltonian introduced by Pryce in paramagnetic resonance is derived up to third-order terms, and the electron-lattice interaction is discussed showing that the Born-Oppenheimer approximation follows from firstorder terms in the case of non-degenerate electronic ground state.