Valleys in Quantum Mechanics
Abstract
Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known results of the interplay of them are reproduced naturally. The prescription for separating the non-perturbative contribution from the perturbative is given in terms of the analytic continuation of the valley parameter. Our method is illustrated on a new series of examples with the asymmetric double-well potential. We obtain the non-perturbative part explicitly, which leads to the prediction of the large order behavior of the perturbative series. We calculate the first 200 perturbative coefficients for a wide range of parameters and confirm the agreement with the prediction of the valley method.
Cite
@article{arxiv.quant-ph/9710064,
title = {Valleys in Quantum Mechanics},
author = {Hideaki Aoyama and Hisashi Kikuchi and Ikuo Okouchi and Masatoshi Sato and Shinya Wada},
journal= {arXiv preprint arXiv:quant-ph/9710064},
year = {2009}
}
Comments
13 pages, 4 eps figures, LaTeX, gzipped tar file