环状Stokes曲线Schrödinger方程的精确WKB分析

Pub Date : 2019-01-01 DOI:10.1619/FESI.62.1

T. Aoki, Kohei Iwaki, Toshinori Takahashi

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引用次数: 13

摘要

研究了具有环型Stokes曲线的Shrödinger-type普通微分方程在大参数下的Stokes现象。为此，我们采用贝塞尔型方程作为标准形式，并计算该方程的Voros系数。结合描述Voros方程的Stokes自同构的公式和连接Shrödinger-type方程与bessel型方程的形式坐标变换，我们得到了描述Shrödinger-type方程WKB解的异导数和Stokes自同构作用的一些公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact WKB Analysis of Schrödinger Equations with a Stokes Curve of Loop Type

Stokes phenomena with respect to a large parameter are investigated for Shrödinger-type ordinary di¤erential equations having a Stokes curve of loop-type. For this purpose, we employ a Bessel-type equation as a canonical form and compute the Voros coe‰cient of the equation. Combining the formula describing the Stokes automorphism for the Voros coe‰cient and the formal coordinate transformation connecting the Shrödinger-type equation and the Bessel-type equation, we have some formulas describing the action of alien derivatives and Stokes automorphism for WKB solutions of the Shrödinger-type equation.

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