Change of Variable as Borel Resummation of Semiclassical Series

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.