Convergence behavior of variational perturbation expansion — A method for locating Bender-Wu singularities

Abstract

Variational perturbation expansions have recently been used by the authors to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence was observed to be exponentially fast with superimposed oscillations. In this note, the observed behavior is explained and used to determine accurately the magnitude and phase of the leading Bender-Wu singularity which is responsible for the finite convergence radius of the strong-coupling expansion in the complex coupling constant plane.