Renormalization-group Resummation of Divergent Series of the Perturbative Wave Function of Quantum Anharmonic Oscillator

Abstract

The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive perturbation series. Working out up to the sixth order and performing a further resummation proposed by Bender and Bettencourt, we find that the agreement with the WKB result becomes worse in the higher orders than the fourth at which the agreement is the best.

Comments: The year in the preprint number is corrected. Two-column version. RevTex 14 pages. No figure