半经典级数Borel恢复时变量的变化
Change of Variable as Borel Resummation of Semiclassical Series
摘要：
它表明，在1维薛定谔方程的变量的变化应用到Borel可求和的基本解决方案[Giller]是相当于Borel重申的基本解决方案乘以适当选择的$\hbar$相关常数。这解释了为什么变量的变化可以改善JWKB公式[Giller，Milczarski]。它还表明，单独的变量的变化不能为我们提供精确的JWKB公式。
英文摘要：
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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