Further Refinements on the Brillouin-Wigner Perturbation Procedure

The first-order correction to the wave function in the Brillouin-Wigner perturbation procedure is generalized by associating independent amplitude coefficients $G_x$ with each physically distinct type of interaction $W^{\mathrm{}\left(x\right)\mathrm{}}$ occurring in the interaction operator. The modified formulas for wave function and energy can be evaluated by using only quantities which occur in the original formulation of the perturbation procedure (characterized by $G_x=1\mathrm{}$). The energy formula is invariant under a transformation which changes the scale of all energy denominators by a constant factor. A uniform displacement of the zeroth-order energy spectrum provides an additional variational parameter.