Change of variables, fundamental solutions and Borel resummation

Physics

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Theory Of Quantized Fields, Solutions Of Wave Equations: Bound States, Field Theory

Scientific paper

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 chosen ℏ-dependent constant. This explains why change of variable can improve JWKB formulas [11]. It is shown also that a change of variable alone cannot provide us with the exact JWKB formulas.

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