Multipoint Levin—Weniger approximants and their application to the ground state energies of quantum anharmonic oscillators

Abstract

If the power series expansions of a function are known about several points, a multipoint approximant can be constructed. One has to solve a set of nonlinear equations to obtain a multipoint Levin—Weniger approximant, whereas in the case of a multipoint Padé approximant one needs to solve only a set of linear equations. This difficulty is overcome by employing a modified linearization prescription used iteratively, as in the case of Levin—Weniger interpolants.The multipoint approximants constructed for some test functions show that they are more effective than multipoint Padé approximants for a given input. We have used two-point Levin—Weniger approximants with information from both the weak and strong coupling perturbation expansions to calculate the ground state energies of quantum anharmonic oscillators. The ground state energies of quartic, sextic and octic anharmonic oscillators are well reproduced over the entire range of the coupling parameter by very simple expressions. It is found that two-point Levin—Weniger approximants reproduce these energies better than two-point Padé approximants.