Change of Variable as Borel Resummation of Semiclassical Series
Quantum Physics
2008-11-26 v2
Abstract
It is shown that a change of variable in 1-dim Schroedinger equation applied to the Borel summable fundamental solutions [Giller] is equivalent to Borel resummation of the fundamental solutions multiplied by suitably chosen -dependent constant. This explains why change of variable can improve JWKB formulae [Giller, Milczarski]. It is shown also that a change of variable alone cannot provide us with the exact JWKB formulae.
Keywords
Cite
@article{arxiv.quant-ph/9712039,
title = {Change of Variable as Borel Resummation of Semiclassical Series},
author = {Stefan Giller and Piotr Milczarski},
journal= {arXiv preprint arXiv:quant-ph/9712039},
year = {2008}
}
Comments
7 pages, uses article.sty art11.sty, 1 EPS figure