Ground state eigenvalue of the anharmonic potential [formula omitted] by high accuracy analytic functions

Abstract

High accuracy analytic functions have been determined for the ground state eigenvalue of the quantum anharmonic potential x4+λx6. The procedure here used is a new application of the multipoint quasi-rational approximation method (MPQA) to quantum mechanics. Previous applications of the technique were performed in the case where the eigenvalues of the potential were already known for the particular case of λ=0. The extension of the method, where this condition is not accomplished, is presented here. As a first step, power and asymptotic expansions have been now also determined. This is followed by the search of a bridge function connecting both expansions, and later the determination of the parameters. Accuracies smaller than 0.1% have been found with only nine parameters.