EFFECTIVE CHARACTERISTIC-POLYNOMIALS AND 2-POINT PADE APPROXIMANTS ASSUMMATION TECHNIQUES FOR THE STRONGLY DIVERGENT PERTURBATION EXPANSIONS OF THE GROUND-STATE ENERGIES OF ANHARMONIC-OSCILLATORS

Pade approximants are able to sum effectively the Rayleigh-Schrodinger perturbation series for the ground state energy of the quartic anharm onic oscillator, as well as the corresponding renormalized perturbatio n expansion [E.J. Weniger, J. Cizek, and F. Vinette, J. Math. Phys. 34 , 571 (1993)]. In the sextic case, Pade approximants are still able to sum these perturbation series, but convergence is so slow that they a re computationally useless. In the octic case, Pade approximants are n ot powerful enough and fail. On the other hand, the inclusion of only a few additional data from the strong coupling domain [E.J. Weniger, A nn. Phys. (N.Y.) (to be published)] greatly enhances the power of summ ation methods. The summation techniques that we consider are two-point Pade approximants and effective characteristic polynomials. It is sho wn that these summation methods give good results for the quartic and sextic anharmonic oscillators, and even in the case of the octic anhar monic oscillator, which represents an extremely challenging summation problem, two-point Pade approximants give relatively good results.