Renormalization-Group Resummation of a Divergent Series of the Perturbative Wave Functions of Quantum Systems

Abstract

The perturbative renormalization group (RG) equation is applied to resum a divergent series of perturbative wave functions of a quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation series. It is shown that a reorganization of the resummed series reproduce the correct asymptotic form of the wave function at cursive Greek chi → ∞ when the perturbation expansion is stopped at the fourth order. A brief comment is given on the relation between the present method and the delta-expansion method, which is based on a kind of nonperturbative RG equation.