These equations have the well-known deficiency that the first order amplitudes become large when there is a neardegeneracy between the zero order ground state and any E (0) I>0 . Thus RS-PT2 is not a regular theory, because E is not bounded from below. The purpose of BW perturbation theory is to avoid this problem. We do not separate the energy by orders in the equations to be solved for the perturbed wavefunction. This one change yields: