Effective-State Approach to 2nd-Order Perturbation-Theory
We show that the complete set of intermediate states in second-order perturbation expressions can be replaced by a finite number of states, provided the subspace they span contains one effective state, solution of an inhomogeneous equation. It is therefore not necessary that the subspace be complete. The existence of this effective state guides the choice of the basis in approximate calculations. As an example, we apply these considerations to two-photon transition rates in hydrogen.