Convergent sequences of perturbative approximations for the anharmonic oscillator I. Harmonic approach

TL;DR

This paper demonstrates that a variational modification of perturbation theory can produce convergent approximations for the quantum anharmonic oscillator, even at strong coupling, with potential extensions to field theories.

Contribution

It introduces a simple variational approach that improves convergence of perturbative approximations in strongly coupled quantum systems.

Findings

Convergent sequences obtained for the anharmonic oscillator

Method effective in the strong coupling limit

Potential applicability to renormalizable field theories

Abstract

We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the purely anharmonic case. Some of the new techniques of this paper can be extended to renormalizable field theories.