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Change of Variable as Borel Resummation of Semiclassical Series

Stefan Giller·Piotr Milczarski
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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.

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Stefan Giller, Piotr Milczarski. 1998-07-14. Change of Variable as Borel Resummation of Semiclassical Series. https://doi.org/10.1088/0305-4470%2F32%2F6%2F009

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