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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 \hbar-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