Perturbation method with triangular propagators and anharmonicities of intermediate strength

Abstract

We propose a new, very flexible version of the Rayleigh–Schrodinger perturbation method which admits a lower triangular matrix in place of the usual diagonal unperturbed propagator. The technique and its enhanced efficiency are illustrated on rational anharmonicities V(1)(x)=β×polynomial(x)/polynomial(x). They are shown tractable, in the intermediate coupling regime, as \(\mathcal{O}(\beta {\text{ - }}\beta ^{{\text{(0)}}} )\) perturbations of exact states at non-vanishing β(0)≠0. In this sense our method bridges the gap between the current weak- and strong-coupling expansions.