A NEW FORM OF RE-ARRANGEMENT OF THE RAYLEIGH-SCHRODINGER PERTURBATION-SERIES

An improvement of convergence of the Rayleigh-Schrodinger perturbation series may be achieved by a ''selfconsistent'' transfer of all the ex cessively large (usually: diagonal) perturbations into denominators. W e propose a new and much more universal realization of such a scheme f or fully general, off-diagonal matrix forms of the zero-order Hamilton ians H-0. A formal core of our recipe lies in a de-diagonalization of Schrodinger operators H-0 - E0I = (I + OMEGA)F(I + OMEGA+) via triangu lar annihilation- and creation-like matrices OMEGA and OMEGA+. Via a p re-partitioning and on- as well as off-diagonal re-arrangement of H-0' s, the standard diagonal ''unperturbed spectrum'' E0 + F is ''smeared' selfconsistently. With tridiagonal or band-matrix H-0's, our new pres cription contains the recently proposed perturbation expansions with c ontinued fractions as a special case.