It is shown that so called fundamental solutions the semiclassical expansions of which have been established earlier to be Borel summable to the solutions themselves appear also to be the unique solutions to the 1D Schrödinger equation having this property. Namely, it is shown in this paper that for the polynomial potentials the Borel function defined by the fundamental solutions can be considered as the canonical one.

It is shown that a change of variable in 1-dim Schrödinger equation applied to the Borel summable fundamental solutions [8,9] is equivalent to Borel resummation of the fundamental solutions multiplied by suitably chosenh-dependent constant. This explains why change of variable can improve JWKB formulae [11]. It is shown also that a change of variable alone cannot provide us with the exact JWKB formulae. PACS number(s): 03.65.-W , 03.65.Sq , 02.30.Lt , 02.30.Mv

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